Discrete Distributions

Find the probability mass function $f\left(x\right)$ of the discrete random variable $X$ whose cumulative distribution function $F\left(x\right)$ is given by $F\left(x\right)=\left\{\begin{array}{lc}0& -\mathrm{\infty }<x<-2\\ 0.25& -2\le x<-1\\ 0.60& -1\le x<0\\ 0.90& 0\le x<1\\ 1& 1\le x<\mathrm{\infty }\end{array}\right.$. Also find $P\left(X<0\right)$.

Find the probability mass function $f\left(x\right)$ of the discrete random variable $X$ whose cumulative distribution function $F\left(x\right)$ is given by $F\left(x\right)=\left\{\begin{array}{lc}0& -\mathrm{\infty }<x<-2\\ 0.25& -2\le x<-1\\ 0.60& -1\le x<0\\ 0.90& 0\le x<1\\ 1& 1\le x<\mathrm{\infty }\end{array}\right.$

Suppose $80\%$ of all families own a television set. If $10$ families are interviewed at random, find the probability that seven families own television 

The probability distribution of a discrete r.v. $X$ is

Find $P(X\le 4)$ and $P (2<X<6)$

A player tosses $2$ fair coins. He wins $₹5$ if $2$ heads appear, $₹2$ if $1$ head appear and $₹1$ if no head appears. Find his expected winning amount and variance of winning amount.

The following is the c.d. f. of a discrete r.v. $X$

Find $P(-1\le X<2)$

The following is the c.d. f. of a discrete r.v. $X$.

Find the p.m.f. of $X$

For the following probability distribution of $X$

Find the probability that $X$ is even

For the following probability distribution of $X$

Find the probability that $X$ is odd.

For the following probability distribution of $X$

Find the probability that $X$ is non-negative

For the following probability distribution of $X$

Find the probability that $X$ is positive.

If the $\mathrm{p}.\mathrm{m}.\mathrm{f}.$ of a random variable $X$ is

then $k=$

If the p.m.f. of a r.v. $X$ is given by $P\left(X=x\right)=\left\{\begin{array}{l}\frac{\left(\begin{array}{l}5\\ x\end{array}\right)}{2^5} , \mathrm{if} x=0,1,2.....5\\ 0 , \text{otherwise}\end{array}\right.$ then which of the following is not true? 

Identify random variables as either discrete or continuous in each of the following situation. Also write the range wherever it is possible

A sample of $10$ batteries are selected and $x=$ number of batteries that failed within 1000 hours.

Identify random variables as either discrete or continuous in each of the following situations. Also write the range wherever it is possible

Four cars are selected from a showroom and $x=$ number of cars having diesel engine.

Identify random variables as either discrete or continuous in each of the following situation. Also write the range wherever it is possible 

A social worker is interested in knowing the number of illiterates in a group of 1000 slum dwellers.

Identify random variables as either discrete or continuous in the following situation. Also, write the range wherever it is possible.

A random variable is number of floors in a building.

Identify random variables as either discrete or continuous in each of the following situation. Also
Write the range wherever it is possible

Number of attempts required by a candidate to clear l.A.S. examination.

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.

Identify random variables as either discrete or continuous in each of the following situation. Also write the range wherever it is possible.  A page in a book can have at most $300$ words. $x=$ Number of misprints on a page.