CUET Mathematics: Applied MathematicsProbability Distribution. Free, no login required.

For 6 trials of an experiment, let X be a binomial variate which satisfies the relation $9P(X=4)=P(X=2)$, then the probability of success is

If $X$ is a Poisson variate such that $P(X=3)=2P(X=4)$, then $P(X=2)$ equals:

[given $e^{-2}=0.14$]

There are 50 telephone lines in an exchange. If the probability that any one of them will be busy is 0.1, then the probability that all the lines are busy is

Which of the following statements are correct?

(A) The mean of a binomial distribution is always greater than the variance.

(B) The mean of a Poisson distribution is always greater than the variance.

(C) If $f(x)$ is the probability density function of a random variable $X$, then $P(a \leq X \leq b) = \int_a^b f(x)dx$.

(D) If $X$ is a random variable and $a,b$ are real numbers, then $Var(aX+b)=a^2Var(X)$.

Choose the correct answer from the options given below:

Let $X$ be a discrete random variable whose probability distribution is defined as follows;

$P(X=x)=\begin{cases}k(x+1), & x=1,2,3,4\\ 2kx, & x=5,6,7\\ 0, & \text{otherwise}\end{cases}$

where $k$ is constant, then $P(X=5)$ is equal to

A coin is tossed until a head appears, or the tail appears 4 times in succession, then the probability distribution of the number of tosses is

The variance of the number of heads in 16 tosses of a coin is

Let the random variable $X$ follow a Poisson distribution. If $P(X=3)=\dfrac{2}{5}P(X=2)$, then $P(X=1)$ is equal to

The probability distribution of a random variable X is given as:

$P(X=x) = \begin{cases} kx^2 & for & x=1,2,3 \\ 2kx & for & x=4,5,6 \\ 0 & otherwise \end{cases}$

Where $k$ is an arbitrary constant, then $E(X)$ is equal to:

If X has a Poisson distribution such that $2P(X=1)=P(X=2)$, then which of the following are correct?

A. The mean of X is 4

B. The mean of X is 2

C. $P(X=2)=\frac{8}{e^4}$

D. $P(X=3)=\frac{32}{e^4}$

Choose the correct answer from the options given below:

In a random experiment, a collection of trials is called Bernoulli trials if

A. The number of trials is infinite.

B. The trials are independent of each other.

C. Each trial has exactly two outcomes, defined as success and failure.

D. The probability of success will vary in each trial.

Choose the correct answer from the options given below:

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $X$ is a Poisson variate such that $4P(X=1)=3P(X=2)$, then $P(X=0)=$

The probability distribution of a random variable $X$ is given as $P(X=x)=\begin{cases}kx^3 & \text{for } x=1,2,3\\ 3kx & \text{for } x=4,5\\ 0 & \text{otherwise}\end{cases}$, where $k$ is a constant.

The value of $P(X\ge4)$ is

If a coin is tossed 8 times and getting a head is considered as success, then which of the following statements are correct ?

(A) The probability of getting 4 heads is $\dfrac{35}{128}$

(B) The mean of the number of successes is 4.

(C) The variance of the number of successes is 2.

(D) The probability of getting 6 heads is $\dfrac{9}{64}$.

Choose the correct answer from the options given below:

Ajay is a vendor who informs that there are 2% rotten apples in the fruit bag. Find the probability that a sample of 10 apples will include not more than one rotten apple.

If the random variable X follows the Poisson distribution such that P[X = k] = P[X = k+1], then the mean value of X is:

The variance of $X$ will be :

The variance of the number of heads in two tosses of a coin is :

10 works hard drawn successively with replacement from a lot containing 10% defective bulb. The probability that there is at least one defective bulb is :

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

then E(X) is equals to

2 voices dice are thrown together. For the first die $P(6) = \frac{1}{2}$, other scores are equally likely. While for the second die $P(1) = \frac{2}{5}$ and other scores are equally likely than the Mean for the probability distribution of the number of one score will be

In a binomial distribution the probability of getting success is $\frac{1}{4}$ And standard deviation is 3 then its mean is ?

$P(X = x) = \begin{cases} 2k & \text{if } x = 0 \\ kx & \text{if } x = 1 \\ k(x - 1) & \text{if } x = 2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$

The value of k is

A random variable X has a probability distribution P(X) of the following form, where k is some unknown constant:

P(X = 0) = k

P(X = 1) = 2k

P(X = 2) = 3k

P(X = other values) = 0

Then, find the value of 1/k.

Match List - I with list- II

Choose the correct option below :

Match list I with list II. 4 defective pens are mixed with 10 normal pens. 3 pens are drawn one by one with replacement , then the probability distribution of the number of defective pens is :

Choose the correct option below :

If the mean of a binomial distribution is 24 and its standard deviation is 4 , then the probability of getting success is :

The random variable X has a probability distribution P(X) of the following form where k is a scalar and

$P(X = x) = \begin{cases} k, & \text{if } x = 0 \\ 2k, & \text{if } x = 1 \\ 3k, & \text{if } x = 2 \\ 0, & \text{otherwise} \end{cases}$

then value of P(X < 2) = _______.

A book consisting of 2000 pages has 540 misprints distributed randomly throughout the book. The average number of misprints in one page of the book is: