Tamil Nadu Board Solutions for Chapter: Probability Distributions, Exercise 6: Exercise 6

The random variable $X$ has the probability density function $f\left(x\right)=\left\{\begin{array}{l}ax+b, 0<x<1\\ 0, \mathrm{otherwise}\end{array}\right.$and $E\left(X\right)=\frac{7}{12}$, then $a$ and $b$ are respectively

Suppose that $X$ takes on one of the values $0,1$and $2$. If for some constant $k, P\left\{X=i\right\}=kP\left\{X=i-1\right\}$ for $i=1,2$ and $P\left\{X=0\right\}=\frac{1}{7}$. Then the value of $k$ is

Which of the following is/are a discrete random variable?

I. The number of cars crossing a particular signal in a day.

II. The number of customers in a queue to buy train tickets at a moment.

III. The time taken to complete a telephone call.

If $f\left(x\right)=\left\{\begin{array}{l}2x, 0\le x\le a\\ 0, \mathrm{otherwise}\end{array}\right.$ is a probability density function of a random variable, then the value of $a$ is

The probability function of a random variable is defined as:

Then $E\left(X\right)$ is equal to:

Let $X$ have a Bernoulli distribution with mean $0.4$, then the variance of $(2X–3)$ is

If in $6$ trials, $X$ is a binomial variate which follows the relation $9P(X=4) = P(X=2)$, then the probability of success is

A computer salesperson knows from his past experience that he sells computers to one in every twenty customers who enter the showroom. What is the probability that he will sell a computer to exactly two of the next three customers?