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Question

A random number generator picks a number from one to thirteen in a uniform manner. Find the following. *note, you will need the f(x) equation to solve c and d*

a) Mean:

b) Standart deviation, round to 4 decimals:

c) Probability that the number chosen is 7;

d) Probability that the number chosen is less than 8.

Answer 1

E(x) = ∑xf(x)

f(x) = 1/13 for i =1 to 13 because it is a uniform distribution

a) µ = ∑_i=1¹³1/13 i = 1/13 ∑_i=1¹³i = 1/13* 13(13+1)/2 = 7

b) var(x) =E(x²) -(E(x))² = 1/13∑_i=1¹³i² - 7² = 1/13(13)(13+1)(2*13+1)/6 - 7² =

63 - 49 = 14

σ = √var = √14 = 3.7417

c) f(x)= 1/13 for i =1to 7 so P(x=7) = f(7) =1/13

d) P(x<8) = f(1)+f(2)+f(3)+f(4)+f(5)+f(6)+f(7) = 7 * 1/13 = 7/13