Question

Suppose that X is a discrete random variable which represents the number of bicycles per household in a town of 1000 households. Consider the following probability distribution below. 1 2 4 0.125 РСХ) 0.256 0.108 0.083 k 21. Determine the value of k and interpret this result. 22. Construct a graph of the probability distribution with appropriate labeling. 23. Find and interpret P(1XS3) 24. Calculate and interpret ux. 25. Calculate and interpret ax.

Answer 1

21 Total pob u 1 & P(x-xi) - 1 PCX=0) + P(x-1) +P(X=2) +P1X=3) +PLX=4)= 1 (9) 0.125+ k + 0.256+ 0.108+ 0.083=1 K+ 0.512=1 1 K= 0.428 Discrete 1 2 3 4 10) PILSX93) - P(x=1) + P(x=2) + P(x=3) = 0.428 + 0.256+ 0.108. 0.792

(d) Mx = E(X)= {X. P(X=x;) - 0X PlX=0)+1.P/X=1) +2. P(X=2) at 3. P(X=3) of Y. P(x-4) = 0 g 0.125 + 1X0.428+ 2 x 0.256 + 3x0.108+ 4x0.082 = 0 + 0.428 +0.512 +0.324 to.332 E(X) - 1.596