Question

Let be a random variable with PDF. Find (round off to the second decimal place):

A) Probability density function
B) Mean value
C) Cumulative distribution function
D) Variance

Answer 1

The student is asking for the PDF, mean, CDF, and variance of a random variable. The correct answer is option D .

Step-by-step explanation:

The student is asking for the probability density function (PDF), mean value, cumulative distribution function (CDF), and variance of a random variable.

A probability density function (PDF) describes the probabilities for a continuous random variable. It represents the likelihood that the variable takes on a specific value. The mean value, also known as the expected value, is the average value of a random variable. The cumulative distribution function (CDF) gives the probability that the variable is less than or equal to a certain value. The variance measures the spread of a random variable.

To find the PDF, you need to integrate the given PDF function over the range of the variable. The mean value is found by multiplying the variable with its PDF and integrating over the range. The CDF is obtained by integrating the PDF from negative infinity to the desired value. The variance is calculated by subtracting the square of the mean value from the mean of the square of the variable.