A random variable X is exponentially distributed with a mean of 0.21. a-1. What is the...

A random variable X is exponentially distributed with a mean of 0.21.

a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.)

a-2. What is the standard deviation of X? (Round your answer to 2 decimal places.)

b. Compute P(X > 0.36). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Expert Solution

In probability theory and statistics, the exponential distribution is the probability distribution that describes the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.

The exponential distribution is not the same as the class of exponential families of distributions, which is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes the normal distribution, binomial distribution, gamma distribution, Poisson, and many others.

a)Rate parameter= λ

E[x]= 1/ λ?

λ= 1/0.21= 4.761

b)Standard Deviation= 1/ λ^2= 4.7619

orchestra answered 1 year ago

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