CUET Mathematics Applied Mathematics > Probability Distribution PYQs

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:

| $ X $ | -2 | -1 | 0 | 1 | 2 | | --- | --- | --- | --- | --- | --- | | $ P(X) $ | $ 0.2 $ | $ 0.1 $ | $ 0.3 $ | $ 0.2 $ | $0.2$ | 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 : | X | 30 | 10 | -10 | |---|---|---|---| | P(X) | 1/5 | 3/10 | 1/2 | 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 | List-I | List - II | |---|---| | A. the probability distribution is applied for discrete random variable | normal distribution | | B. A normal distribution is symmetric about | standard deviation | | C. this probability distribution is applied for continuous random variable | mean | | D. the shape of normal curve depend upon | Poisson distribution | 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 : | List-I | List - II | |---|---| | A. P(X=0) | 8/343 | | B. P(X=1) | 60/343 | | C. P(X=2) | 125/343 | | D. P(X=3) | 150/343 | 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:

The variance of the Binomial Distribution $B\left(5, \frac{1}{4}\right)$ is:

A shopkeeper wants to check the average number of cars sold per call. Past record of sales is shown below: | Sale of cars (Units) | 0 | 1 | 2 | 3 | |---|---|---|---|---| | Probabilities | $\frac{1}{6}$ | $\frac{1}{2}$ | $\frac{3}{10}$ | $\frac{1}{30}$ | The expected number of cars sold is :

If the mean of a binomial distribution is 12 and its standard deviation is 2, then the number of trials is :

If the probability distribution of X is : | X | 2 | 3 | 4 | 5 | 6 | |---|---|---|---|---|---| | P(X) | 1/15 | 2/15 | 3/15 | 4/15 | 5/15 | Then variance is equal to :

If a random variable X follows binomial distribution with mean 5 and variance $\frac{5}{2}$, then $P(X \leq 9)$ is :

Which of the following statements are correct ? (A) $\text{var}(aX + b) = a^2 \text{var}(X)$ (B) $\text{var}(X) = E(X^2) - \{E(X)\}^2$ (C) $E(aX + b) = aE(X) + b$ (D) $E(X) = \sum_{i=1}^{n} p_i x_i^2$ Choose the correct answer from the options given below :

In binomial distribution with $n = 10$ and $P = \frac{1}{3}$, the probability of the event that unequal number of failures and successes occur is :

The probability distribution of a random variable X is given below : | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.1 | 0.25 | 0.3 | 0.2 | 0.15 | Then, $\text{Var}\left(\frac{X}{2}\right)$ is :

If X has a Poisson distribution such that $P(X = 1) = P(X = 2)$ then $P(X = 3)$ is :

A discrete random variable X has the following probability distribution : | X: | 0 | 1 | 2 | 3 | 4 | 5 | |----|----|----|----|----|----|----| | P(X): | b | 3b | 5b | 3b | 4b | 6b | The value of b is :

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If $P(X=1) = 0.4$, $P(X=4) = P(X=2)$ and $P(X=3) = 2P(X=2)$, then $P(X=0)$ is :

A telephone exchange receives on an average 5 calls per minute. The probability of receiving 3 or less calls per minute is :

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) In a binomial distribution, if $n = 10$, $q = 0.25$, then its mean is | (I) 12 | | (B) If the mean of a binomial distribution is 6 and its variance is 3, then p is | (II) 7.5 | | (C) In a binomial distribution, the probability of getting a success is $\frac{1}{4}$ and the standard distribution is 3, then its mean is | (III) 16 | | (D) If the mean and variance of a binomial distribution are 4 and 3 respectively, then the number of trials is | (IV) $\frac{1}{2}$ | Choose the correct answer from the options given below :

If the sum and product of the mean and variance of a binomial distribution are 18 and 72 respectively, then the probability of obtaining atmost one success is

Between 3 p.m. and 5 p.m. the average number of phone calls per minute coming into the helpline desk of a bank is 5. The probability that during one particular minute there will be only one phone call is :

Match List I with List II | LIST I | LIST II | |---|---| | A. The variance of a Poisson distribution with mean $\lambda$ is | I. $\sqrt{\lambda}$ | | B. The standard deviation of a Poisson distribution with mean $\lambda$ is | II. 4 | | C. In a Poisson distribution, if mean is 4, then the standard deviation is | III. $\lambda$ | | D. In a Poisson distribution, if mean is 4, then the variance is | IV. 2 | Choose the correct answer from the options given below:

If the probability distribution of a discrete random variable $X$ is given as | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.5 | 2k | 3k | 3k | 2k | Then the value of $k$ is:

If the probability distribution of a random variable X is given as | $x_i$ | 0 | 1 | 2 | 3 | |---|---|---|---|---| | $p_i$ | $2k^2$ | $k^2$ | $3k^2$ | $k$ | Then the mean of X is