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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.

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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

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