Home
Class 12
MATHS
A coin is tossed thrice. X denotes the n...

A coin is tossed thrice. X denotes the no. of heads appeared. Find the mean and variance of X.

Text Solution

Verified by Experts

S={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
P(X=0)`=1/2xx1/2xx1/2=1/8`
P(X=1) `=1/2xx1/2xx1/2+1/2xx1/2xx1/2+1/2xx1/2xx1/2=3/8`
P(X=2) `=1/2xx1/2xx1/2+1/2xx1/2xx1/2+1/2xx1/2xx1/2=3/8`
P(X=3) `=1/2xx1/2xx1/2=1/8`

`E(X)=1/8xx0+3/8xx1+3/8xx2+1/8xx3=3/2`
`E(X^2)=1/8xx0+3/8xx1+3/8xx4+1/8xx9=3`
`Var(X)=E(X^2)-(E(X))^2`
`=3-9/4=3/4`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    AAKASH INSTITUTE|Exercise TRY YOURSELF|36 Videos

  • PROBABILITY

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION - A Competition Level Questions)|114 Videos

  • PRINCIPLE OF MATHEMATICAL

    AAKASH INSTITUTE|Exercise Section-D:(Assertion-Reason Type Questions)|12 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos

Similar Questions

Explore conceptually related problems

A die is tossed thrice . A success I is or 6 on a toss. Find the mean and variance of successes.

A coin is tossed 4 times. Let X denote the number of heads. Find the probability distribution of X. Also, find the mean and variance of X.

A coin is tossed thrice. If event E denotes the number of heads is odd and event F denotes the number of tails is odd, then find the cases favourable to the event EnnF .

A fair coin is tossed 4 times. If X denotes the number of heads obtained, then the formula for p.m.f. of X is

A coin is tossed thrice. If E be the event of showing at least two heads and F be the event of showing head in the first throw, then find P(E/F) .

A fair coin is tossed 3 times. Let X be the number of heads obtained. Find E(X) and V(X).

A die is tossed thrice. A success is getting 5 or 6 on a toss. The mean and the variance of number of successes

A fair coin is tossed four xx.Let X denote the number of heads occurring.Find the probability distribution,mean and variance of X.

A coin is tossed three times .If X denotes the absolute difference between the number of heads and the number of tails then P (X=1)=