Question

In: Statistics and Probability

The duration of a phone call is modeled by using an exponential random variable with variance...

The duration of a phone call is modeled by using an exponential random variable with variance 4.5 hours2. If the duration of the phone call has already lasted for 9 minutes, then what is the probability that the duration of the phone call will last at least 65 minutes?

Solutions

Expert Solution

The probability that the duration of the phone call will last at least 65 minutes given that the call has already lasted for 9 minutes is 0.64410.

The detailed answer is attached in the form of image.


Related Solutions

For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability...
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability density function. Given that the expected lifetime of this machine is 10 years, find the exponential probability density function f(t) for random variable T
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability...
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability density function. Given that the expected lifetime of this machine is 10 years, find the exponential probability density function f(t) for random variable T
Suppose X is an exponential random variable with mean 5 and Y is an exponential random...
Suppose X is an exponential random variable with mean 5 and Y is an exponential random variable with mean 10. X and Y are independent. Determine the coefficient of variation of X + Y
Question 1. For each random variable, state whether the random variable should be modeled with a...
Question 1. For each random variable, state whether the random variable should be modeled with a Binomial distribution or a Poisson distribution. Explain your reasoning. State the parameter values that describe the distribution and give the probability mass function. Random Variable 1. A quality measurement for cabinet manufacturers is whether a drawer slides open and shut easily. Historically, 2% of drawers fail the easy slide test. A manufacturer samples 10 drawers from a batch. Assuming the chance of failure is...
Q1. (A) Explain the exponential random variable and normal random variable with at-least ten examples in...
Q1. (A) Explain the exponential random variable and normal random variable with at-least ten examples in real life? In which situation we prefer normal random variable instead of exponential variable? (B) Find the Mean, variance and cumulative density function for following probability density function as: (state your results in detail computation) f(w)=10 e-10w ; 0≤w≤∞
The following measurements were recorded for the duration, in seconds, of phone calls in a call-center...
The following measurements were recorded for the duration, in seconds, of phone calls in a call-center of a major corporation: 30        32        27        20 32        30        26        30 33 29 1. the mode of the dataset is: 26 s                  b)   27 s           c)   30 s           d)   32 s           e)    33 s The median of the dataset is: 30.15 s             b)   28.9 s        c)   30 s           d)   28.9 s2       e)   30 s2 The mean of the duration of the phone call...
Probability And Statistics Question: Explain the exponential random variable and normal random variable with at-least ten...
Probability And Statistics Question: Explain the exponential random variable and normal random variable with at-least ten examples in real life? In which situation we prefer normal random variable instead of exponential variable?
Recall the lifetime (in months) of a battery is modeled by a random variable X that...
Recall the lifetime (in months) of a battery is modeled by a random variable X that has pdf fθ(x)=Kθx1(x>0)where K=ln(1/θ) for an unknown parameter θ∈(0,1) . Assume instead that we cannot actually observe the lifetime of the batteries. Instead, we only observe if the battery is still working after τ months for some known τ to be chosen later (this is called censored data ). Let Y1,…,Yn be our observations where Yi=1(Xi>τ) indicates that the i th battery is still...
Using I.uniform,II binomial , III. exponential and IV. Poisson random variable for each solve the following...
Using I.uniform,II binomial , III. exponential and IV. Poisson random variable for each solve the following A. What is the average of the 500 sample means when the sample size is n = 5? What is the average of the 500 sample means when the sample size is n = 50? What are the theoretical expected values of sample means, respectively? b. For n = 5 and n = 50, what are the variances of the 500 sample means, respectively?...
Create a problem where the given is about a random variable that is exponential. Ask a...
Create a problem where the given is about a random variable that is exponential. Ask a question that requires the exponential distribution & solve. Ask a question that requires the use of the Poisson & solve. (Note – problem 4 gives information about a Poisson random variable and then asks Poisson and exponential questions.)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT