12th Business Maths Weekly Test - 2 ( Random Variable and Mathematical expectation )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 2 ( 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

The probability density function p(x) cannot exceed

zero
one
mean
infinity

In the probability mass function for getting 3's when two dice are thrown, which of the following is incorrect?

P(X = 0) = \(\frac { 25 }{ 36 }\)
P(X = 1) = \(\frac { 10 }{ 36 }\)
P(X = 3) = \(\frac { 1 }{ 36 }\)
P(X = 2) = \(\frac { 1 }{ 36 }\)

A B

1. If x \(\ge\) 0, then E(X) a. aE(X)

2. E(a X + b) b. a

3. E(a) c. 0

4. E(aX) d. aE(X) + b

The correct match is

1-c, 2-d, 3-b, 4-a
1-a, 2-b, 3-c,4-d
1-b, 2-c, 3-d, 4-a
1-d, 2-a, 3-b, 4-c

In a discrete probability distribution the sum of all the probabilities is always equal to

zero
one
minimum
maximum

A formula or equation used to represent the probability distribution of a continuous random variable is called

probability distribution
distribution function
probability density function
mathematical expectation

A random variable X has the following probability mass function

X -2 3 1

P(X=x) \(\frac { λ }{ 6 } \) \(\\ \frac { λ }{ 4 } \) \(\frac { λ }{ 12 } \)

Then λ is

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

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

If cis a constant, then E(c) is

0
1
c f(c)
c

Which one is not an example of random experiment?

A coin is tossed and the outcome is either a head or a tail
A six-sided die is rolled
Some number of persons will be admitted to a hospital emergency room during any hour.
All medical insurance claims received by a company in a given year.

Which of the following is not possible in probability distribution?

\(\sum { p(x)\ge 0 } \)
\(\sum { p(x)=1 } \)
\(\sum { xp(x)=2 } \)
\(p(x)=-0.5\)

X is a discrete random variable. Which take values 0,1,2 and P(X = 0) = \(\frac { 144 }{ 169 }\) , P(X = 1) = \(\frac { 1 }{ 169 }\) ,then the value of P(X = 2) is

\(\frac { 145 }{ 169 }\)
\(\frac { 24}{ 169 }\)
\(\frac { 2 }{ 169 }\)
\(\frac { 143 }{ 169 }\)

In the following distribution function

X 1 2 3 4 5 6

F(X) \(\frac { 1 }{ 6 }\) \(\frac { 2 }{ 6 }\) \(\frac { 3 }{ 6 }\) \(\frac { 4 }{ 6 }\) \(\frac { 5 }{ 6 }\) 1

A B

1. P(X=1) a. \(\frac { 1 }{ 6 }\)

2. P(X \(\le\) 2) b. \(\frac { 3 }{ 6 }\)

3. P(X=5) c. \(\frac { 2 }{ 6 }\)

4. P(X \(\ge\) 4) d. \(\frac { 1 }{ 6 }\)

The correct match is

1-a, 2-b, 3-c, 4-d
1-b, 2-c, 3-d, 4-a
1-c, 2-d, 3-a, 4-b
1-a, 2-c, 3-d, 4-b

Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0⋅ 29, 0⋅ 40, 0⋅ 35. Pofit per unit is 0⋅ 50 paisa then expected profits for three days are

21, 19, 22
21.5, 19.5, 22.5
0.29, 0.40, 0.35
3.045, 3.8, 3.85

\(\overset { \infty }{ \underset { -\infty }{ \int } } \)f(x)dx is always equal to

zero
one
E(X)
f(x) +1

Part - B

Generic 5 - Answer All Question

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)

Determine the mean and variance of the random variable Xhaving the following probability distribution.

X=x 1 2 3 4 5 6 7 8 9 10

P(x) 0.15 0.10 0.10 0.01 0.08 0.01 0.05 0.02 0.28 0.20

The probability distribution of a random variation X is given below.

X 0 1 2 3 4

P(X) 0.1 0.25 0.3 0.2 0.15

Find (i) V(X) (ii) v\(\left( \frac { X }{ 2 } \right) \)

If f (x) is defined by f(x)=k2-2x, 0\(\le\)x<\(\infty\)is a density function. Determine the constant k and also find mean.

Suppose the life in hours of a radio tube has the probability density function
f(x)={\({ e }^{ \frac { x }{ 100 } },when\quad x\ge 100\\ 0,\quad when\quad x<100\)
Find the mean of the life of a radio tube.

The following information is the probability distribution of successes.

No. of Successes 0 1 2

Probability \(\frac{6}{11}\) \(\frac{9}{22}\) \(\frac{1}{22}\)

Determine the expected number of success.

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.
An urn contains four balls of red, black, green and blue colours. There is an equal probability of getting any coloured ball. What is the expected value of getting a blue ball out of 30 experiments with replacement?

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	A		B
1.	If x \(\ge\) 0, then E(X)	a.	aE(X)
2.	E(a X + b)	b.	a
3.	E(a)	c.	0
4.	E(aX)	d.	aE(X) + b

X	-2	3	1
P(X=x)	\(\frac { λ }{ 6 } \)	\(\\ \frac { λ }{ 4 } \)	\(\frac { λ }{ 12 } \)

X	1	2	3	4	5	6
F(X)	\(\frac { 1 }{ 6 }\)	\(\frac { 2 }{ 6 }\)	\(\frac { 3 }{ 6 }\)	\(\frac { 4 }{ 6 }\)	\(\frac { 5 }{ 6 }\)	1

	A		B
1.	P(X=1)	a.	\(\frac { 1 }{ 6 }\)
2.	P(X \(\le\) 2)	b.	\(\frac { 3 }{ 6 }\)
3.	P(X=5)	c.	\(\frac { 2 }{ 6 }\)
4.	P(X \(\ge\) 4)	d.	\(\frac { 1 }{ 6 }\)

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

No. of Successes	0	1	2
Probability	\(\frac{6}{11}\)	\(\frac{9}{22}\)	\(\frac{1}{22}\)

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12th Business Maths Weekly Test - 2 ( Random Variable and Mathematical expectation )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 2 ( 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

The probability density function p(x) cannot exceed

In the probability mass function for getting 3's when two dice are thrown, which of the following is incorrect?

A B 1. If x \(\ge\) 0, then E(X) a. aE(X) 2. E(a X + b) b. a 3. E(a) c. 0 4. E(aX) d. aE(X) + b The correct match is

In a discrete probability distribution the sum of all the probabilities is always equal to

A formula or equation used to represent the probability distribution of a continuous random variable is called

A random variable X has the following probability mass function X -2 3 1 P(X=x) \(\frac { λ }{ 6 } \) \(\\ \frac { λ }{ 4 } \) \(\frac { λ }{ 12 } \) Then λ is

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

If cis a constant, then E(c) is

Which one is not an example of random experiment?

Which of the following is not possible in probability distribution?

X is a discrete random variable. Which take values 0,1,2 and P(X = 0) = \(\frac { 144 }{ 169 }\) , P(X = 1) = \(\frac { 1 }{ 169 }\) ,then the value of P(X = 2) is

Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0⋅ 29, 0⋅ 40, 0⋅ 35. Pofit per unit is 0⋅ 50 paisa then expected profits for three days are

\(\overset { \infty }{ \underset { -\infty }{ \int } } \)f(x)dx is always equal to

Part - B

Generic 5 - Answer All Question

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)

Determine the mean and variance of the random variable Xhaving the following probability distribution. X=x 1 2 3 4 5 6 7 8 9 10 P(x) 0.15 0.10 0.10 0.01 0.08 0.01 0.05 0.02 0.28 0.20

The probability distribution of a random variation X is given below. X 0 1 2 3 4 P(X) 0.1 0.25 0.3 0.2 0.15 Find (i) V(X) (ii) v\(\left( \frac { X }{ 2 } \right) \)

If f (x) is defined by f(x)=k2-2x, 0\(\le\)x<\(\infty\)is a density function. Determine the constant k and also find mean.

Suppose the life in hours of a radio tube has the probability density function f(x)={\({ e }^{ \frac { x }{ 100 } },when\quad x\ge 100\\ 0,\quad when\quad x<100\) Find the mean of the life of a radio tube.

The following information is the probability distribution of successes. No. of Successes 0 1 2 Probability \(\frac{6}{11}\) \(\frac{9}{22}\) \(\frac{1}{22}\) Determine the expected number of success.

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.

An urn contains four balls of red, black, green and blue colours. There is an equal probability of getting any coloured ball. What is the expected value of getting a blue ball out of 30 experiments with replacement?

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Tamilnadu Stateboardszs - Class

A B

1. If x \(\ge\) 0, then E(X) a. aE(X)

2. E(a X + b) b. a

3. E(a) c. 0

4. E(aX) d. aE(X) + b

The correct match is

A random variable X has the following probability mass function

X -2 3 1

P(X=x) \(\frac { λ }{ 6 } \) \(\\ \frac { λ }{ 4 } \) \(\frac { λ }{ 12 } \)

Then λ is

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)

Determine the mean and variance of the random variable Xhaving the following probability distribution.

X=x 1 2 3 4 5 6 7 8 9 10

P(x) 0.15 0.10 0.10 0.01 0.08 0.01 0.05 0.02 0.28 0.20

The probability distribution of a random variation X is given below.

X 0 1 2 3 4

P(X) 0.1 0.25 0.3 0.2 0.15

Find (i) V(X) (ii) v\(\left( \frac { X }{ 2 } \right) \)

Suppose the life in hours of a radio tube has the probability density function
f(x)={\({ e }^{ \frac { x }{ 100 } },when\quad x\ge 100\\ 0,\quad when\quad x<100\)
Find the mean of the life of a radio tube.

The following information is the probability distribution of successes.

No. of Successes 0 1 2

Probability \(\frac{6}{11}\) \(\frac{9}{22}\) \(\frac{1}{22}\)

Determine the expected number of success.

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.