Suppose that the probability distribution of a random variable x can be describe

Question

Suppose that the probability distribution of a random variable x can be described by the formula P(x) = x/15 for each of the values x =1, 2, 3, 4, and 5, e.g., p(x = 2) = 2 /15. Write out the probability distribution of x in tabular form (Keep p(x) in Fractions format!). Answer the following questions.

a) Find p(x < 3)

b) Calculate the expected value (mean) Note: plug in the original fractions from the tabular form, and round the FINAL ANSWER to the THIRD decimal place.

c) Calculate the standard deviation Note: plug in the original fractions from the tabular form, and round the FINAL ANSWER to the THIRD decimal place.

d) Compute the interval ( – 2, + ) Note: round to the THIRD decimal place.

Lower Limit =

Upper Limit =

e) Find the actual probability (in DECIMAL format) that x falls within the interval of part d)

Explanation / Answer

X 1 2 3 4 5 P(X) 0.06666666667 0.1333333333 0.2 0.2666666667 0.3333333333 x*P(X) 0.06666666667 0.2666666667 0.6 1.066666667 1.666666667 x^2*P(X) 0.06666666667 0.5333333333 1.8 4.266666667 8.333333333 E(X) 3.6667 E(X^2) 15 variance 1.555555556 standard deviation 1.247219129 upperlimit 4.9139 lower limit 1.1722

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