. Suppose X ∼ Unif(−1, 3). Find the probabilities of the following events, both by hand calculation and with R’s punif function. (a) (X ≤ 2) (b) (X ≥ 1) (c) (−0.5 < X < 1.5) (d) (X = 0)

a)

b)

c)

d)

Step-by-step explanation:

Let X the random variable of interest and we know that the distribution is given by:

And for this problem we can use the cumulative distribution function in order to solve the items:

Part a

We want to find this probability:

Part b

Part c

And we can calculate the probability with this difference:

Part d

Since we have a continuous distribution the the probability for an unique value would be:

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.