List of top Mathematics Questions on Probability Distribution asked in AP EAPCET

The following table gives the probability distribution of a random variable \(X\): \[ \begin{array}{|c|c|c|c|c|} \hline x_i & 0 & 1 & 2 & 3 \\ \hline P(X=x_i) & 0.1 & 0.3 & 0.5 & 0.1 \\ \hline \end{array} \] The standard deviation of \(X\) is:

If the probability function of a random variable \(X\) is \[ P(X=x)=ak^x,\qquad x=0,1,2,\ldots, \] then the value of \(k\) is

A random variable X takes values 0, 1, 2, 3 and its mean is 1.3. If $P(X=3)=2P(X=1)$ and $P(X=2)=0.3$, then find $P(X=0)$.

In a binomial distribution with 5 trials, the probabilities of 1 success and 2 successes are 0.4096 and 0.2048 respectively. Find the variance of the distribution.

A dice is thrown twice. If getting a number greater than four is considered a success, the variance of the probability distribution of the number of successes is

If the mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then \( P(X=2)= \)

Consider the random experiment of throwing a die and tossing a coin. Let \[ \{(a,b)\mid a\in\{H,T\},\ b\in\{1,2,\ldots,6\}\} \] denote the outcomes of the experiment. If $X$ is a random variable defined by \[ X(a,b)=b, \] then the variance of $X$ is

If $X\sim B(n,p)$ is a binomial variate, $8p^2+15p-2=0$ and the product of the mean and variance of $X$ is $\dfrac78$, then $P(X=4)=$

A random variable $X$ has the following probability distribution:
$X = x$: 0, 1, 2, 3, 4, 5
$P(X=x)$: $k$, $3k$, $5k$, $7k$, $9k$, $11k$
Then the value of $k$ is:

In a binomial distribution, the mean is 4 and the variance is 3. Then the number of trials $n$ is:

The discrete random variables \(X\) and \(Y\) are independent from one another and are defined as \(X \sim B(n_1, 0.5)\) and \(Y \sim B(n_2, 0.4)\). If the variance of both \(X\) and \(Y\) is 6, then \(\sqrt{n_1+n_2} =\)

The probability that A wakes up before the alarm rings is 0.4. Then, the mean and variance of the number of times A wakes up before the alarm rings in the next 7 days, respectively are:

During the winter months in a certain village in Scotland, the probability of a day having severe fog is \(0.6\). The probability that in a given week there will be exactly two days with severe fog is:

Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the 10 pages selected at random will have no print mistakes is:

The maximum value of the variance of Binomial distribution with parameters \(n\) and \(p\) is:

The random variable \(X\) has Binomial distribution \[ B(20,0.4) \] Then \[ 5-5P(X\geq 2)= \] is equal to:

A multiple choice test consists of \(5\) questions, each question having \(4\) responses. There is only one correct response and the remaining \(3\) are incorrect responses. If a candidate attempts all the \(5\) questions, then the probability that he answers at least \(3\) questions incorrectly is