12th Business Maths Weekly Test - 1 ( Random Variable and Mathematical expectation )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 1 ( Random Variable and Mathematical expectation )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

Probability which explains x is equal to or less than particular value is classified as

discrete probability
cumulative probability
marginal probability
continuous probability

An expected value of a random variable is equal to it's

variance
standard deviation
mean
covariance

If f(x) = cx², 0 < x < 2 is the p.d.f. of x, then c is

\(\frac { 1 }{ 3 }\)
\(\frac { 4 }{ 3 }\)
\(\frac { 8 }{ 3 }\)
\(\frac { 3 }{ 8 }\)

If the p.d.f of a continuous random variable. X is f(x) = \(\begin{cases} \frac { x }{ 2 } ,\quad \quad 0<x<2 \\ 0,\quad elsewhere \end{cases}\) then E(3X²-2x) =

\(\frac { 2 }{ 3 }\)
\(\frac { 4 }{ 3 }\)
\(\frac { 10 }{ 3 }\)
\(\frac { 7 }{ 3 }\)

\(\mu \)_2=20,\(\mu ^{ 1 }_{ 2 }\)=276 for a discrete random variable. X. Then the mean of the random variable. X is

If the random variable takes negative values, then the negative values will have

positive probabilities
negative probabilities
constant probabilities
difficult to tell

E[X-E(X)] is equal to

E(X)
V(X)
0
E(X)-X

Two coins are tossed simultaneously. The values of a, b, c in the probability distribution

No of heads 0 1 2

Probability a b c

are_____________.

\(\frac { 1 }{ 3 },\frac { 3 }{ 4 },0\)
\(0,\frac { 3 }{ 4 },\frac { 1 }{ 4 }\)
\(\frac { 3 }{ 2 },\frac { 1 }{ 2 },\frac { 1 }{ 4 }\)
\(\frac { 1 }{ 4 },\frac { 2 }{ 4 },\frac { 1 }{ 4 }\)

The probability density function p(x) cannot exceed

zero
one
mean
infinity

If we have f(x)=2x, 0\(\le\)x\(\le\)1, then f (x) is a

probability distribution
probability density function
distribution function
continuous random variable

Part - B

Generic 2 - Answer All Question

Find the mean for the probability density function

f(x)= \(\begin{cases} \frac { 1 }{ 24, } \quad -12\le x\le 12 \\ 0,\quad otherwise \end{cases}\)

Describe what is meant by a random variable.

A continuous random variable X has the following probability function

Value of X=x 0 1 2 3 4 5 6 7

P(x) 0 k 2k 2k 3k k² 2k² 7k²+k

(i) Find k

(ii) Evaluate P(x < 6), P(x\(\ge \) 6) and P(0 < x < 5)

(iii) If P(X \(\le \) x) > 12 then find the minimum value of x.
The probability function of a random variable X is given by

p(x) = \(\begin{cases} \frac { 1 }{ 4 } ,\quad for\quad x=-2 \\ \frac { 1 }{ 4 } ,\quad for\quad x=0 \\ \frac { 1 }{ 2 } ,\quad for\quad x=10 \\ 0,\quad elsewhere \end{cases}\)

Evaluate the following probabilities.
(i) P(X\(\le\)0), (ii) P(X < 0),
(iii) P(\(|\)X\(|\)\(\le\)2) and (iv) P(0\(\le\)X\(\le\)10)

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function

f(x) = \(\begin{cases} 2{ e }^{ -2x },\quad x\quad >\quad 0 \\ 0,\quad otherwise \end{cases}\)

Find the expected life of this piece of equipment.

Distinguish between discrete and continuous random variable.

Part - C

Generic 3 - Answer All Question

A random variable. X has following distribution

X -1 0 1 2

P (X = x) \(\frac13\) \(\frac16\) \(\frac16\) \(\frac13\)

Find E(2X+3)²

If the probability density function of a random variable. X is given by f(x) =\(\frac{2x}{9}\), 0 < x < 3 then find E(3 X +8).

Two cards are drawn from a pack of 52 playing cards. Find the probability distribution of the number of aces.

If you toss a fair coin three times, the outcome of an experiment consider as random variable which counts the number of heads on the upturned faces. Find out the probability mass function and check the properties of the probability mass function.

If a random variable. X has the probability distribution

X 0 1 2 3 4 5

P (X = x) a 2a 3a 4a 5a 6a

then find F(4)
A player tosses two unbiased coins. He wins Rs.5 if two heads appear, Rs.2 if one head appear and Rs.1 if no head appear. Find the expected amount to win.

Part - D

Generic 5 - Answer All Question

The probability density function of a random variable X is
f(x)=ke^-|x|, -∞<x< ∞
Find the value of k and also find mean and variance for the random variable.

The probability distribution of a random variable X is

X 1 2 4 2A 3A 5A

P(X) \(\frac { 1 }{ 2 } \) \(\frac15\) \(\frac{3}{25}\) \(\frac { 1 }{ 10 } \) \(\frac { 1 }{ 25 } \) \(\frac { 1 }{ 25 } \)

Calculate (i) A if E(X) = 2.94 (ii) V(X)

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function.
f(x)={\({ 3e }^{ -3x },\quad x>0\\ 0,otherwise\)
Find the expected life of the piece of equipment.

A fair die is thrown. Find out the expected value of its outcomes

Comment

Add Comment

X	1	2	4	2A	3A	5A
P(X)	\(\frac { 1 }{ 2 } \)	\(\frac15\)	\(\frac{3}{25}\)	\(\frac { 1 }{ 10 } \)	\(\frac { 1 }{ 25 } \)	\(\frac { 1 }{ 25 } \)

Value of X=x	0	1	2	3	4	5	6	7
P(x)	0	k	2k	2k	3k	k²	2k²	7k²+k

InstaQB

Institutions

12th Standard English Medium

12th Standard Tamil Medium

11th Standard English Medium

11th Standard Tamil Medium

10th Standard English Medium

9th Standard English Medium

8th Standard English Medium

7th Standard English Medium

Class XII

Class XI

12Th Standard

11Th Standard

10Th Standard

9Th Standard

12th Business Maths Weekly Test - 1 ( Random Variable and Mathematical expectation )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 1 ( Random Variable and Mathematical expectation )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

Probability which explains x is equal to or less than particular value is classified as

An expected value of a random variable is equal to it's

If f(x) = cx2, 0 < x < 2 is the p.d.f. of x, then c is

If the p.d.f of a continuous random variable. X is f(x) = \(\begin{cases} \frac { x }{ 2 } ,\quad \quad 0<x<2 \\ 0,\quad elsewhere \end{cases}\) then E(3X2-2x) =

\(\mu \)2=20, \(\mu ^{ 1 }_{ 2 }\)=276 for a discrete random variable. X. Then the mean of the random variable. X is

If the random variable takes negative values, then the negative values will have

E[X-E(X)] is equal to

Two coins are tossed simultaneously. The values of a, b, c in the probability distribution No of heads 0 1 2 Probability a b c are_____________.

The probability density function p(x) cannot exceed

If we have f(x)=2x, 0\(\le\)x\(\le\)1, then f (x) is a

Part - B

Generic 2 - Answer All Question

Find the mean for the probability density function f(x)= \(\begin{cases} \frac { 1 }{ 24, } \quad -12\le x\le 12 \\ 0,\quad otherwise \end{cases}\)

Describe what is meant by a random variable.

A continuous random variable X has the following probability function Value of X=x 0 1 2 3 4 5 6 7 P(x) 0 k 2k 2k 3k k2 2k2 7k2+k (i) Find k (ii) Evaluate P(x < 6), P(x\(\ge \) 6) and P(0 < x < 5) (iii) If P(X \(\le \) x) > 12 then find the minimum value of x.

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function f(x) = \(\begin{cases} 2{ e }^{ -2x },\quad x\quad >\quad 0 \\ 0,\quad otherwise \end{cases}\) Find the expected life of this piece of equipment.

Distinguish between discrete and continuous random variable.

Part - C

Generic 3 - Answer All Question

A random variable. X has following distribution X -1 0 1 2 P (X = x) \(\frac13\) \(\frac16\) \(\frac16\) \(\frac13\) Find E(2X+3)2

If the probability density function of a random variable. X is given by f(x) =\(\frac{2x}{9}\), 0 < x < 3 then find E(3 X +8).

Two cards are drawn from a pack of 52 playing cards. Find the probability distribution of the number of aces.

If you toss a fair coin three times, the outcome of an experiment consider as random variable which counts the number of heads on the upturned faces. Find out the probability mass function and check the properties of the probability mass function.

If a random variable. X has the probability distribution X 0 1 2 3 4 5 P (X = x) a 2a 3a 4a 5a 6a then find F(4)

A player tosses two unbiased coins. He wins Rs.5 if two heads appear, Rs.2 if one head appear and Rs.1 if no head appear. Find the expected amount to win.

Part - D

Generic 5 - Answer All Question

The probability density function of a random variable X is f(x)=ke-|x|, -∞<x< ∞ Find the value of k and also find mean and variance for the random variable.

The probability distribution of a random variable X is X 1 2 4 2A 3A 5A P(X) \(\frac { 1 }{ 2 } \) \(\frac15\) \(\frac{3}{25}\) \(\frac { 1 }{ 10 } \) \(\frac { 1 }{ 25 } \) \(\frac { 1 }{ 25 } \) Calculate (i) A if E(X) = 2.94 (ii) V(X)

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function. f(x)={\({ 3e }^{ -3x },\quad x>0\\ 0,otherwise\) Find the expected life of the piece of equipment.

A fair die is thrown. Find out the expected value of its outcomes

Comment

Other Study material

12th Business Maths Weekly Test - 3 ( Operations R

12th Business Maths Weekly Test - 4 ( Operations R

12th Business Maths Monthly Test - 1 ( Operations

12th Business Maths Monthly Test - 2 ( Operations

12th Business Maths Weekly Test - 5 ( Sampling tec

12th Business Maths Monthly Test - 1 ( Sampling te

12th Business Maths Weekly Test - 1 ( Sampling tec

12th Business Maths Weekly Test - 2 ( Sampling tec

12th Business Maths Weekly Test - 3 ( Sampling tec

12th Business Maths Weekly Test - 4 ( Sampling te

12th Business Maths Weekly Test - 4 ( Applied Stat

12th Business Maths Weekly Test - 3 ( Applied Stat

12th Business Maths Weekly Test - 2 ( Applied Stat

12th Business Maths Weekly Test - 1 ( Applied Stat

12th Business Maths Monthly Test - 3 ( Sampling te

Tamilnadu Stateboardszs - Class

If f(x) = cx², 0 < x < 2 is the p.d.f. of x, then c is

If the p.d.f of a continuous random variable. X is f(x) = \(\begin{cases} \frac { x }{ 2 } ,\quad \quad 0<x<2 \\ 0,\quad elsewhere \end{cases}\) then E(3X²-2x) =

\(\mu \)_2=20,\(\mu ^{ 1 }_{ 2 }\)=276 for a discrete random variable. X. Then the mean of the random variable. X is

Two coins are tossed simultaneously. The values of a, b, c in the probability distribution

No of heads 0 1 2

Probability a b c

are_____________.

Find the mean for the probability density function

f(x)= \(\begin{cases} \frac { 1 }{ 24, } \quad -12\le x\le 12 \\ 0,\quad otherwise \end{cases}\)

A continuous random variable X has the following probability function

Value of X=x 0 1 2 3 4 5 6 7

P(x) 0 k 2k 2k 3k k² 2k² 7k²+k

(i) Find k

(ii) Evaluate P(x < 6), P(x\(\ge \) 6) and P(0 < x < 5)

(iii) If P(X \(\le \) x) > 12 then find the minimum value of x.

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function

f(x) = \(\begin{cases} 2{ e }^{ -2x },\quad x\quad >\quad 0 \\ 0,\quad otherwise \end{cases}\)

Find the expected life of this piece of equipment.

A random variable. X has following distribution

X -1 0 1 2

P (X = x) \(\frac13\) \(\frac16\) \(\frac16\) \(\frac13\)

Find E(2X+3)²

If a random variable. X has the probability distribution

X 0 1 2 3 4 5

P (X = x) a 2a 3a 4a 5a 6a

then find F(4)

The probability density function of a random variable X is
f(x)=ke^-|x|, -∞<x< ∞
Find the value of k and also find mean and variance for the random variable.

The probability distribution of a random variable X is

X 1 2 4 2A 3A 5A

P(X) \(\frac { 1 }{ 2 } \) \(\frac15\) \(\frac{3}{25}\) \(\frac { 1 }{ 10 } \) \(\frac { 1 }{ 25 } \) \(\frac { 1 }{ 25 } \)

Calculate (i) A if E(X) = 2.94 (ii) V(X)

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function.
f(x)={\({ 3e }^{ -3x },\quad x>0\\ 0,otherwise\)
Find the expected life of the piece of equipment.