# Tag: probability distribution

#### Solved (Free): Let $Y_1, Y2, \cdots, Y_n$ be independent random variables such that each $Y_i$ has a gamma distribution with parameters

Let $Y_1, Y2, \cdots, Y_n$ be independent random variables such that each $Y_i$ has a gamma distribution with parameters $\alpha_i$ and $\beta$. That is, the distributions of the $Y$'s might…

#### Solved: The time between release from prison and the commission of another crime is uniformly distributed between 0 and 5 years for a high-risk group

The time between release from prison and the commission of another crime is uniformly distributed between 0 and 5 years for a high-risk group. Give the equation and graph the…

#### Solved: The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants”

The article "Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants" (Water Research [1984]: 1169-1174) suggests the uniform distribution on the interval from 7.5 to 20 as a model for…

#### Solved: The hardness of a piece of ceramic is proportional to the firing time. Assume that a rating system has been devised to rate the hardness of a ceramic piece

The hardness of a piece of ceramic is proportional to the firing time. Assume that a rating system has been devised to rate the hardness of a ceramic piece and…

#### Solved: Suppose that a class in elementary statistics was allocated 15 minutes to complete a quiz. It can be assumed that the time X it takes to complete

Suppose that a class in elementary statistics was allocated 15 minutes to complete a quiz. It can be assumed that the time X it takes to complete the quiz is…

#### 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 (Free): A western city has 18 police officers eligible for promotion. Eleven of the 18 are Hispanic

A western city has 18 police officers eligible for promotion. Eleven of the 18 are Hispanic. Suppose only five of the police officers are chosen for promotion and that one…

#### Solved:The first assignment in a statistical computing class involves running a short program. If past experience indicates

The first assignment in a statistical computing class involves running a short program. If past experience indicates that 40% of all students will make no programming errors, compute the (approximate)…

#### Solved (Free): False-positives in testing for HIV. A rapid test for the presence in the blood of antibodies to HIV, the virus that causes

False-positives in testing for HIV. A rapid test for the presence in the blood of antibodies to HIV, the virus that causes AIDS, gives a positive result with probability about…