InstaQB

Home
Institutions
- Institutions
  
  Polytechnic Colleges
  
  Medical Colleges
  
  Arts & Science Colleges
  
  Universities
  
  Engineering Colleges
  
  Agricultural Colleges
  
  Research Institute
  
  Law Colleges
  
  Audiology and Speech Colleges
  
  Business & Management colleges
  
  Nursing colleges
  
  Hotel Management institutes
  
  Aeronautical Colleges
  
  Bachelor's Degree
Syllabus
Courses
Stateboard
- 12th Standard English Medium
  
  Maths
  
  Physics
  
  Chemistry
  
  Biology
  
  Computer Science
  
  Business Maths
  
  Economics
  
  Commerce
  
  Accountancy
  
  History
  
  Computer Applications
  
  Computer Technology
  12th Standard Tamil Medium
  
  உயிரியல்
  
  கணினி பயன்பாடுகள்
  
  கணினி அறிவியல்
  
  வணிகக் கணிதம்
  
  வணிகவியல்
  
  பொருளியல்
  
  கணிதவியல்
  
  வேதியியல்
  
  இயற்பியல்
  
  கணினி தொழில்நுட்பம்
  
  வரலாறு
  
  கணக்குப்பதிவியல்
  11th Standard English Medium
  
  Maths
  
  Commerce
  
  Economics
  
  Biology
  
  Business Maths
  
  Accountancy
  
  Computer Science
  
  Physics
  
  Chemistry
  
  Computer Applications
  
  History
  
  Computer Technology
  
  Bio - Zoology
  11th Standard Tamil Medium
  
  கணிதவியல்
  
  உயிரியல்
  
  பொருளியல்
  
  இயற்பியல்
  
  வேதியியல்
  
  வணிகக் கணிதம்
  
  கணினி அறிவியல்
  
  கணக்குப்பதிவியல்
  
  வணிகவியல்
  
  கணினி பயன்பாடுகள்
  10th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  9th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  8th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  7th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
ICSE/ISC
- Class XII
  
  Mathematics
  
  Physics
  
  Accountancy
  
  Biology
  
  History
  
  Geography
  
  Psychology
  
  chemistry
  
  Economics
  
  Computer Science
  
  Political Science
  
  Business Studies
  Class XI
  
  Accountancy
  
  Chemistry
  
  Mathematics
  
  Biology
  
  Geography
  
  Physics
  
  History
CBSE
- 12Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Geography
  
  Socialogy
  
  Business Studies
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  
  Home Science
  11Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Socialogy
  
  Business Studies
  
  Geography
  
  Home Science
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  10Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  Mathematics
  
  Economics
  
  Geography
  
  History & Civics
  
  Computer Application
  9Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  mathematics
  
  Computer Application
  
  Economics
  
  Geography
  
  History & Civics

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

St. Britto Hr. Sec. School - Madurai

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

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

variance
standard deviation
mean
covariance

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) = \(\frac { 1 }{ 36 }\)

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

zero
one
minimum
maximum

If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to

Σf(x)
Σf[x + f(x)]
Σf(x) + x
Σxp(x)

A variable that can assume any possible value between two points is called

discrete random variable
continuous random variable
discrete sample space
random variable

A discrete probability function p(x) is always

non-negative
negative
one
zero

A discrete random variable. X has the probability mass function p(x), then _______ is true.

0 \(\le\) P(X) \(\le\) 1
P(X) \(\ge\) 0
P(X) \(\le\) 1
0 < P (X) < 1

A listing of all the outcomes of an experiment and the probability associated with each outcome is called

probability distribution
probability density function
attributes
distribution function

Which of the following are correct?

(i) E(aX+b) = a E(X) + b
(ii) \(\mu \)₂ = \(\mu \)₂¹ - (\(\mu \)₁¹)²
(iii) \(\mu \)₂= variance
(iv) V (a X + b) = a² V (x)

all
i, ii and iii
ii and iii
i and iv

The height of persons in a country is a random variable of the type

discrete random variable
continuous random variable
both (a) and (b)
neither (a) nor (b)

A B

1. S.D of X a. \(\sigma { x }^{ 2 }\)

2. V(x) b. \(\overset { \infty }{ \underset { -\infty }{ \int } } \)x.f(x)dx

3. E(X²) - [E(X)]² c. + \(\sqrt { Var(x) } \)

4. E(X) d. V(X)

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

If c is a constant in a continuous probability distribution, then p(x = c) is always equal to

zero
one
negative
does not exist

If X is a continuous random variable., then which of the following is incorrect?

F'(x)=f(x)
F(\(\infty \))= 1, F(-\(\infty \)) = 0
P(a \(\le\) X \(\le\) b) = F(b) - F(a)
P(a \(\le\) X < b) \(\neq \) F(b) - F(a)

If f(x) = kx(1- x), 0< x < 1 is a p.d.f. then the value of k is ___________.

\(\frac { 1 }{ 5 }\)
\(\frac { 2 }{ 5 }\)
\(\frac { 3 }{ 5 }\)
6

Given E(X +c ) =8 and E(X- c) = 12, then the value of c is

-2
4
-4
2

Part - B

Generic 2 - Answer All Question

In a business venture a man can make a profit of Rs.2,000 with a probability of 0.4 or have a loss of Rs.1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?

Explain the terms
(i) probability mass function,
(ii) probability density function and
(iii) probability distribution function.

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)

What is the expected value of game that works as follows : I flip a coin and, if tails pay you Rs.2; if heads pay you Rs.1. In either case I also pay you Rs.50.

A discrete random variable. X has the following probability distribution

X 0 1 2 3 4 5 6 7 8

P (X) a 3a 5a 7a 9a 11a 13a 15a 17a

Find the value of a and P(X < 3)

Two eggs are drawn at random without replacement from a bag containing two bad eggs and eight good eggs. Find the probability of getting two bad eggs ?

A continuous random variable X has the following distribution function:
F(x)={\(0\quad \quad \quad \quad ,if\quad x\le 1\\ k(x-1{ ) }^{ 4 },if13\)
Find (i) k and (ii) the probability density function.

The probability function of a random variable X is given by
p(x)={\(\frac { 1 }{ 4 } ,\quad for\quad x=-2\\ \frac { 1 }{ 4 } ,\quad for\quad x=0\\ \frac { 1 }{ 2 } ,\quad for\quad x=10\\ 0,\quad elsewhere\)
Evaluate the following probabilities.
(i) P(\(\le\))0,
(ii) P(X<0)
(iii) P(|X|\(\le\)2) and
(iv) P(0\(\le\)X\(\le\)10)

A person tosses a coin and is to receive Rs. 4 for a head and is to pay Rs. 2 for a tail. Find the expectation and variance of his gains.
Describe what is meant by a random variable.

State the definition of Mathematical expectation using continuous random variable.

Construct cumulative distribution function for the given probability distribution.

X 0 1 2 3

P(X = x) 0.3 0.2 0.4 0.1

How do you define variance in terms of Mathematical expectation?

In an investment, a man can make a profit of Rs. 5,000 with a probability of 0.62 or a loss of Rs.8,000 with a probability of 0.38. Find the expected gain.

The discrete random variable X has the following probability function

P(X=x) =\(\begin{cases} \quad \quad kx\quad x=2,4,6 \\ k(x - 2)\quad \quad x=8 \\ \quad \quad 0\quad otherwise \end{cases}\)

where k is a constant. Show that k = \(\frac {{ 1 }}{{ 18 }} \)

Define Mathematical expectation in terms of discrete random variable.

Part - C

Generic 3 - Answer All Question

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 random variable X can take all nonnegative integral values and the probabilities that X takes the value r is proportional to a^r (0 < a < 1). Find P(X = 0).

An urn contains 4 white and 6 red balls. Four balls are drawn at random from the urn. Find the probability distribution of the number of white balls.

Suppose, the life in hours of a radio tube has the following p.d.f
f(x)=\(\frac { 100 }{ { x }^{ 2 } } ,when\quad \ge 100\\ 0,\quad when\quad x<100\)
Find the distribution function.
A continuous random variable X has p.d.f
f(x)=5x⁴,0\(\le\)x\(\le\)1
Find a1 and a2 such that i) P[X\(\le\)a₁]=P[X>a₁] ii) P[X>a₂]=0.05

Construct the distribution function for the discrete random variable X whose probability distribution is given below. Also draw a graph of p(x) and F(x).

X = x 1 2 3 4 5 6 7

P(x) 0.10 0.12 0.20 0.30 0.15 0.08 0.05

The probability distribution of a discrete random variable. X is given by

X -2 2 5

P (X = x) \(\frac14\) \(\frac14\) \(\frac12 \)

then find 4E(X²) - Var (2X)

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.

A random variable X has the following probability function

Values of X 0 1 2 3 4 5 6 7

p(x) 0 a 2a 2a 3a a² 2a² 7a²+a

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 \(p(x)\begin{cases} \underline { x } , \\ 20 \\ 0, \end{cases}x=\)0,1,2,3,4,5
Find (i) P(X<3) and (ii) P(2\(\le\)4)

Part - D

Generic 5 - Answer All Question

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.

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

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.
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.

Determine the mean and variance of a discrete random variable, given its distribution as follows.

X=x 1 2 3 4 5 6

F_x(x) \(\frac{1}{6}\) \(\frac{2}{6}\) \(\frac{3}{6}\) \(\frac{4}{6}\) \(\frac{5}{6}\) 1

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?

Comment

Add Comment

Tamilnadu Stateboardszs - Class