Question

In: Statistics and Probability

If the duration of the songs follows a beta distribution, with a range two and a...

If the duration of the songs follows a beta distribution, with a range two and a half to five minutes, with parameters Alpha = 3 and beta = 3
A) Find the probability that the duration of a randomly selected song is greater than 4.2 minutes. (10 pts)

B) Find the average and variance of the duration of the songs (remember that it is not standard Beta and that it needs to be adjusted) (15 pts)

Solutions

Expert Solution

Let X be a random variable that denotes the duration of the song.

It is given that

The PDF of X is given as:

where in minutes.

(A) So, the required probability is given as:



(B) Now the transformation used when we are standardising is:

where Z is the standard beta variable.

By formula,

Thus, the mean is given by:

Also, by formula

Thus, the variance is given by:

orchestra answered 3 years ago
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