EASY

Earn 100

Identify random variables as either discrete or continuous in each of the following situation. Also write the range wherever it is possible. Number of students present in a class of $50$ students.

Important Questions on Probability Distributions

HARD

Mathematics>Algebra>Probability Distributions>Discrete Distributions

Suppose

A

3 \times 3

matrix consisting of integer entries that are chosen at random from the set

\{- 1000, - 999, \dots 999, 1000\} .

Let

P

be the probability that either

A^{2} = - I

A

is diagonal, where

I

is the

3 \times 3

identity matrix. Then,

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

A random variable $X$ has the following probability distribution

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P (X)$	$K - 1$	$3 K$	$K$	$3 K$	$3 K^{2}$	$K^{2}$	$K^{2} + K$

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

Let

x_{i} (1 \leq i \leq 10)

be ten observation of a random variable

X

. If

\sum_{i = 1}^{10} (x_{i} - p) = 3

and

\sum_{i = 1}^{10} {(x_{i} - p)}^{2} = 9

where

0 \neq p \in R

, then the standard deviation of these observations is:

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

From a lot of

30

bulbs which include

6

defectives, a sample of

4

bulbs are drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

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 =

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

For the probability distribution given by

$X = x_{i}$	$0$	$1$	$2$
$P_{i}$	$25 / 36$	$5 / 18$	$1 / 36$

The standard deviation $(σ)$ is

HARD

Mathematics>Algebra>Probability Distributions>Discrete Distributions

If '

X

' has a binomial distribution with parameters

n = 6, p

and

P (X = 2) = 12, P (X = 3) = 5

, then

p =

HARD

Mathematics>Algebra>Probability Distributions>Discrete Distributions

A cubical die is thrown. Find the mean and variance of

X

, giving the number on the face that shows up.

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

A boy tosses fair coin

3

times. If he gets ₹

2 x

for

x

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

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

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,

EASY

Mathematics>Algebra>Probability Distributions>Discrete Distributions

A random variable $X$ has the probability distribution :

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P (X)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

For the events

E = \{X is a prime number\}

and

F = \{X < 4\},

then

P (E \cup F)

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

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 the value of $λ$ is

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

A random variable

X

takes the values

0, 1, 2

. Its mean is

1.2

P (X = 0) = 0.3

, then

P (X = 1) =

EASY

Mathematics>Algebra>Probability Distributions>Discrete Distributions

Given below is the probability distribution of discrete random variable $X$

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$
$P [X = x]$	$K$	$0$	$2 K$	$5 K$	$K$	$3 K$

Then, $P [X \geq 4] =$

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

A random variable $X$ has the following probability distribution:

$X = x_{i}$	$- 2$	$- 1$	$0$	$1$	$2$
$P (X = x_{i})$	$\frac{1}{6}$	$k$	$\frac{1}{4}$	$k$	$\frac{1}{6}$

The variance of this random variable is

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

A random variable $X$ has the following probability distribution.

$\begin{array}{lcccccccc} X = x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ P (X = x) & 0 & k & 2 k & 2 k & 3 k & k^{2} & 2 k^{2} & 7 k^{2} + k \end{array}$

Find $k$ . [Write your answer in decimal]

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

A random variable $X$ has the following probability distribution.

$\begin{array}{lcccccccc} X = x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ P (X = x) & 0 & k & 2 k & 2 k & 3 k & k^{2} & 2 k^{2} & 7 k^{2} + k \end{array}$

Find $k$ . [Write your answer in decimal]

EASY

Mathematics>Algebra>Probability Distributions>Discrete Distributions

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:

HARD

Mathematics>Algebra>Probability Distributions>Discrete Distributions

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 :

MEDIUM

Mathematics>Algebra>Probability Distributions>Discrete Distributions

A die is rolled. If

X

denotes the number of positive divisors of the outcome then the range of the random variable

X

Identify random variables as either discrete or continuous in each of the following situation. Also write the range wherever it is possible. Number of students present in a class of 50 students.

Important Questions on Probability Distributions

Learn and Prepare for any exam you want !

Identify random variables as either discrete or continuous in each of the following situation. Also write the range wherever it is possible. Number of students present in a class of $50$ students.