Consider a uniform distribution that is defined for 1 ≤ X ≤ 5 . a. Sketch the distribution. b. What is the probability that X falls below 1.5? c. What is the probability that X lies above 2.5? d. What

a)

The density function for this case is given by:

And the distribution is on the figure attached

b)

And for this case we can use the cumulative distribution function given by:

And if we use this formula we got:

c)

And we can use the complement rule and the cimulative distribution function and we can rewrite the expression like this:

d)

Step-by-step explanation:

Part a

For this case we define the random variable X and the distribution for X is given by:

The density function for this case is given by:

And the distribution is on the figure attached

Part b

For this case we want this probability:

And for this case we can use the cumulative distribution function given by:

And if we use this formula we got:

Part c

For this case we want this probability:

And we can use the complement rule and the cimulative distribution function and we can rewrite the expression like this:

Part d"  What is the probability that X lies below 1?

And for this case we can use the cumulative distribution function given by:

And if we use this formula we got:

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