Question

Problem 2: Suppose the amount of liquid dispensed by a machine is uniformly distributed with lower limit A 8 oz and upper limit B 10 oz. If the amount of liquid dispensed by consecutive use are independent, define X to be the total amount of liquid dispensed by the machine after being used twice. (a) What is the probability distribution of X? (b) What is the mean and variance of X? (c) What is the probability that the total amount is liquid dispensed is between 17 and 19 oz? (d) What is the probability of the total amount being dispensed is greater than 19 07

Answer 1

Answer:

a).

After 2 use, X follows uniform distribution with A=16 and B=20.

b).

Expectation = (a + b)/2 = 18

Variance = (b - a)²/12 = 1.3333

Standard deviation = 1.1547

c).

P( 17<x<19) = P( x <19) – P( x <17)

= 0.75- 0.25

=0.50

d).

P( x >19) = 0.25