Question

The random variable x has the discrete probability distribution shown here: x -2 -1 0 1 2 p(x) 0.1 0.15 0.4 0.3 0.05 1) Find P(x<2) Please use up to 4 decimal places and use the proper uses of rounding. Excel can be a helpful calculator in these problems. 2) Find the expected value (mean) of this discrete random variable. Please use up to 4 decimal places and use the proper rules of rounding. Excel can be a helpful calculator in these problems.

Solution :

From given discrete probability distribution ,

1)

P(X < 2) = 0.1 + 0.15 + 0.4 + 0.3 = 0.95

2)

Mean = X * P(X)

=  -2 * 0.1 + - 1 * 0.15 + 0 * 0.4 + 1 * 0.3 + 2 * 0.05 = 0.05

Expected value = 0.05

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