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Let X denote the number of times ‘a total of 9’ appears in two throws of a pair of dice. Find the probability distribution of X. Also, find the mean, variance and standard deviation of X.

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Given : Let X denote the number of times ‘a total of 9’ appears in two throws of a pair of dice

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

Formula used :

When a die is tossed twice,

Total possible outcomes =

Let X denote the number of times ‘a total of 9’ appears in two throws of a pair of dice

Two dice are tossed twice, hence n = 2

The probability distribution table is as follows,

The probability distribution table is as follows,

Mean = \(\frac{2}{9}\)

Variance = \(\frac{16}{81}\)

Standard deviation = \(\frac{4}{9}\)

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