Question

# Suppose X is a random variable whose probability distribution is given by the following table: X...

Suppose X is a random variable whose probability distribution is given by the following table: X 0 2 4 6 P(X) 0.11 0.12 0.52 0.25 For each item below, write the capital letter which corresponds to the correct value. Some letters may not be used and some letters may be used more than once. • P(X is even)? • P(X < 4)? • P(X ≤ 4)? • P(X 6= 2)? • P(X = 2 and X = 6)? • P(1 < X < 3)? • Mean/Expected value of X? • Variance of X? • Standard deviation of X? A. 0.00 B. 0.12 C. 0.23 D. 0.34 E. 0.75 F. 0.88 G. 0.89 H. 1.00 I. 1.79 J. 3.28 K. Insufficient information

a) P(X is even) = P(X = 2) + P(X = 4) + P(X = 6) = 0.12 + 0.52 + 0.25 = 0.89

b) P(X < 4) = P(X = 0) + P(X = 2) = 0.11 + 0.12 = 0.23

c) P(X < 4) = P(X = 0) + P(X = 2) + P(X = 4) = 0.11 + 0.12 + 0.52 = 0.75

d) P(X not 2) = 1 - P(X = 2) = 1 - 0.12 = 0.88

e) P(X = 2 and X = 6) = 0

f) P(1 < X < 3) = P(X = 2) = 0.12

g) Mean = E(X) = 0 * 0.11 + 2 * 0.12 + 4 * 0.52 + 6 * 0.25 = 3.82

h) E(X2) = 02 * 0.11 + 22 * 0.12 + 42 * 0.52 + 62 * 0.25 = 17.8

Variance = E(X2) - (E(X))2 = 17.8 - 3.822 = 3.2076 = 3.21

i) Standard deviation = sqrt(3.2076) = 1.79

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