Question

In: Statistics and Probability

Let x be an exponential random variable with lambda equals 0.2. Calculate the probabilities described below....

Let x be an exponential random variable with lambda equals 0.2. Calculate the probabilities described below.

a. ​P(x<7​)

b. ​P(x>8​)

c. ​P(7< = x < = 8​)

d. ​P(x> = 6​)

e. the probability that x is at most 8

Solutions

Expert Solution

This Problem is solved by using R

X ~ Exponential( lambda=0.2)
X is continuous distribution so at a certain point probability equal to zero therefore P(X<x)=P(X<=x)

Answer :

a. ​P(x<7​) = 0.753403

b. ​P(x>8​)=0.2018965

c. ​P(7< = x < = 8​) =0.04470045

d. ​P(x> = 6​) =0.3011942

e. the probability that x is at most 8 =P(x<=8) = 0.7981035

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