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Suppose $X$ is normal with mean $6$ . If $P (X > 16) = 0.0228$ , then what is the variance of $X$ ? [Use $Φ (2) = 0.9772$ ]

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Important Questions on Probability Distributions

HARD

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

Let a pair of dice be thrown and the random variable

X

be the absolute value of the difference of the numbers that appear on the two dice. The expectation value

E (X)

X

EASY

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

A discrete random variable $X$ takes values $10, 20, 30$ and $40$ , with probability $0.3, 0.3, 0.2, 0.2$ respectively. Then the expected value of $X$ is

EASY

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

Given

E (X + c) = 8

and

E (X - c) = 12

. Then the value of

c

EASY

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

In a random experiment of throwing

5

coins, the number of heads is defined as a random variable. The mean of the random variable is

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

The p. d. f. of a random variable

x

is given by

f (x) = \{\begin{cases} \frac{1}{4 a}, (a > 0) & 0 < x < 4 a, \\ 0, & Otherwise \end{cases}

and

P (x < \frac{3 a}{2}) = k P (x > \frac{5 a}{2})

then

k = \dots \dots

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

A six faced die is biased such that

3 \times P

(a prime number)

= 6 \times P

(a composite number)

= 2 \times P (1)

. Let

X

be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of

X

EASY

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

Variance of the random variable

X

4

. Its mean is

2

. Then

E (X^{2})

is:

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

A boy tosses fair coin

3

times. If he gets ₹

2 x

for

x

heads then his expected gain equals to ₹........

HARD

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

Let

X

be a random variable such that the probability function of a distribution is given by

P (X = 0) = \frac{1}{2}, P (X = j) = \frac{1}{3^{j}} (j = 1, 2, 3, \dots, \infty) .

Then the mean of the distribution and

P (X

is positive and even

)

respectively, are:

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

A box contains

6

red ball and

2

black balls. Two balls are drawn at random from it without replacement. If

X

denotes the number of red balls drawn, then

E (X)

is equal to

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

Find the mean number of heads in three tosses of a fair coin:

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

The mean and standard deviation of random variable

X

are

10

and

5

respectively, then

E {(\frac{X - 15}{5})}^{2} =

_________.

HARD

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

In a game, a man wins Rs.

100

if he gets

5

6

on a throw of a fair die and loses Rs.

50

for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

EASY

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

Let

X

be a random variable having binomial distribution

B (7, p)

. If

P (X = 3) = 5 P (X = 4)

, then the sum of the mean and the variance of

X

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

A box contains

6

pens,

2

of which are defective. Two pens are taken randomly from the box. If random variable

x :

Number of defective pens obtained, then standard deviation of

x =

EASY

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

A random variable

X

has the following probability distribution:

\begin{matrix} \begin{matrix} X : & 1 & \begin{matrix} 2 & 3 & \begin{matrix} 4 & 5 \end{matrix} \end{matrix} \end{matrix} \\ P (X) : \begin{matrix} k^{2} & \begin{matrix} 2 k & k & \begin{matrix} 2 k & 5 k^{2} \end{matrix} \end{matrix} \end{matrix} \end{matrix}

Then,

P (X > 2)

is equal to:

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

An unbiased coin is tossed

5

times. Suppose that a variable

X

is assigned the value

k

when

k

consecutive heads are obtained for

k = 3, 4, 5,

otherwise

X

takes the value

- 1 .

Then the expected value of

X,

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

For the random variable $X$ with probability distribution is given by the table

$X = x$	$0$	$1$	$2$	$3$
$P (X = x)$	$K$	$K + \frac{1}{7}$	$2 K$	$\frac{2}{5}$

The mean of $X$ is

MEDIUM

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

What is the mean of $f (x) = 3 x + 2$ where $x$ is a random variable with probability distribution

$X = x$	$1$	$2$	$3$	$4$
$P (X = x)$	$\frac{1}{6}$	$\frac{1}{3}$	$\frac{1}{3}$	$\frac{1}{6}$

HARD

Mathematics>Algebra>Probability Distributions>Mathematical Expectation

If the height of the

300

students is normally distributed with mean

64.5

inches and standard deviation

3.3

inches, find the height below which

99 %

of the students lie

(P [0 < z < 2.33] = 0.49)

Suppose X is normal with mean 6. If P(X>16)=0.0228, then what is the variance of X? [Use Φ(2)=0.9772]

Important Questions on Probability Distributions

Learn and Prepare for any exam you want !

Suppose $X$ is normal with mean $6$ . If $P (X > 16) = 0.0228$ , then what is the variance of $X$ ? [Use $Φ (2) = 0.9772$ ]