Question

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.

Answer 1

Given : A coin is tossed 4 times

To find : probability distribution of X and mean (μ) and variance (σ²)

Formula used :

A coin is tossed 4 times,

Total possible outcomes = 2⁴ = 16

X denotes the number of heads

Let p be the probability of getting a head,

since the coin is tossed 4 times, n = 4

X can take the values of 1,2,3,4

The probability distribution table is as follows,

The probability distribution table is as follows,

Mean = 2

Variance = 1