Question

A continuous random variable X is uniformly distributed in an interval (−1,4). A new random variable Y is described as:

a) The square of X

b) The absolute value of X

c) The reciprocal of X

d) The sum of X and a constant term c

Answer 1

The random variable X is uniformly distributed in the interval (-1,4) and X~ can represent various transformations of X. The probability distribution of X is a rectangle with a height of 1/5, and the distribution is a uniform distribution.

Step-by-step explanation:

a. The random variable X represents a continuous random variable that is uniformly distributed in the interval (-1,4). It means that any value between -1 and 4 (excluding -1 and 4) is equally likely to occur.

b. The random variable X~ can be used to represent any of the given options: the square of X, the absolute value of X, the reciprocal of X, or the sum of X and a constant term c.

c. The probability distribution of a uniform distribution is a rectangle, where the height of the rectangle represents the probability density and the width represents the interval. In this case, the height of the rectangle is 1/5 (since the interval width is 4 - (-1) = 5).

d. The distribution is a uniform distribution.