Question

Assume that a continuous random variable X is uniformly distributed over the interval

1
a) 0b) 2c) 2d) 1

Answer 1

The random variable X is a continuous random variable uniformly distributed over the interval (0,2). The probability distribution for this uniform distribution is a rectangle with equal probabilities for all values between 0 and 2.

Step-by-step explanation:

The random variable X is defined as a continuous random variable that is uniformly distributed over the interval (0,2). This means that any value between 0 and 2, including the endpoints, has an equal chance of being chosen.

The probability distribution graph of this uniform distribution would be a rectangle with the height equal to the reciprocal of the width, which is 2-0 = 2 in this case. The total area under the rectangle is 1, since the sum of all probabilities must be equal to 1.

Therefore, the distribution is a uniform probability distribution.