Problem 1E

Let Y be a random variable with p(y) given in the table below.

a Give the distribution function, F(y). Be sure to specify the value of F(y) for all y,−∞ < y < ∞.

b Sketch the distribution function given in part (a).

Solution 1E

Step1 of 3:

We have random variable Y and it probability values are given below:

y |
1 |
2 |
3 |
4 |

P(y) |
0.4 |
0.3 |
0.2 |
0.1 |

Here our goal is:

a). We need to give the distribution function, F(y). here the value of F(y) for all y, −∞ < y < ∞.

b). We need to sketch the distribution function given in part (a).

Step2 of 3:

a).

The distribution function of F(y) is given by:

Now,

Step3 of 3:

b).

The graph of the given distribution function is given by: