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Three cards are drawn successively with replacement from a well – shuffled deck of 52 cards. A random variable X denotes the number of hearts in the three cards drawn. Find the mean and variance of X.

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Given : Three cards are drawn successively with replacement from a well – shuffled deck of 52 cards.

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

Formula used :

Three cards are drawn successively with replacement from a well – shuffled deck of 52 cards.

Let X be the number of hearts drawn.

Number of hearts in 52 cards is 13

The probability distribution table is as follows,

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