Question

# A continuous random variable X is uniformly distributed. The minimum value for X is 20 and...

A continuous random variable X is uniformly distributed. The minimum value for X is 20 and the maximum value for X is 120.

1. Write down the rules for f(x), the density function for X.

2. Find the median of this distribution.

3. Find P(X>40)

4. Find P( 25 < X < 55)

5. Find P(X < 75)

a) We are given here that the distribution is uniform from 20 to 120, therefore the distribution here is given as:

Therefore the probability density function for X here is obtained as:

This is the required PDF here.

b) The median of the distribution here is computed as:

Therefore 70 is the required median here.

c) The probability here is computed as:

Therefore 0.8 is the required probability here.

d) The probability here is computed as:

Therefore 0.3 is the required probability here.

e) The probability here is computed as:

Therefore 0.55 is the required probability here.

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