Question

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

Answer 1

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