# Tag: exponential distribution

#### Solved:The lifetime $X$ of a device is an exponential random variable with mean = $1/R$

The lifetime $X$ of a device is an exponential random variable with mean = $1/R$. Suppose that due to irregularities in the production process, the parameter $R$ is random and…

#### Solved: The useful life of an electrical component is exponentially distributed with a mean of 2,500 hours

The useful life of an electrical component is exponentially distributed with a mean of 2,500 hours. a. What is the probability the circuit will last more than 3,000 hours? b.…

#### Solved: The amount of time that a union stays on strike is judged to follow an exponential distribution with a mean

The amount of time that a union stays on strike is judged to follow an exponential distribution with a mean of 10 days. a. Find the probability that a strike…

#### Solved: If the number of minutes that a doctor spends with a patient is a random variable having an exponential distribution

If the number of minutes that a doctor spends with a patient is a random variable having an exponential distribution with the parameter $\theta = 9$, what are the probabilities…

#### Solved: The amount of time, in hours, that a machine functions before breakdown is a continuous random variable with pdf

The amount of time, in hours, that a machine functions before breakdown is a continuous random variable with pdf \begin{aligned} f(t) &= \frac{1}{120} e^{-t/120}, t\geq 0 \end{aligned} What…

#### Solved: The time required to pass through security screening at the airport can be annoying to travelers

The time required to pass through security screening at the airport can be annoying to travelers. The mean wait time during peak periods at Cincinnati/Northern Kentucky International Airport is 12.1…

#### Solved: The number of years a radio functions is exponentially distributed with parameter

The number of years a radio functions is exponentially distributed with parameter $\lambda =1/8$. If Jones buys a used radio, what is the probability that it will be working after…

#### Solved: The lifetimes in years for a particular brand of cathode ray tube are exponentially distributed with a mean of 5 years

The lifetimes in years for a particular brand of cathode ray tube are exponentially distributed with a mean of 5 years. What percent of the tubes have lifetimes between 5…