Determine the cumulative distribution function for the random variable in Exercise 3-17; also determine the following probabilities:

Step 1 of 4:

The table is given below.

x |
-2 |
-1 |
0 |
1 |
2 |

f(x) |
0.2 |
0.4 |
0.1 |
0.2 |
0.1 |

Then the cumulative distribution function for the given data:

x |
f(x) |
F(x) |

-2 |
0.2 |
0.2 |

-1 |
0.4 |
0.2+0.4 = 0.6 |

0 |
0.1 |
0.6+0.1 = 0.7 |

1 |
0.2 |
0.7+0.2 = 0.9 |

2 |
0.1 |
0.9+0.1 = 1.0 |

The resultant cumulative distribution function for the given data is

Our goal is:

We need to determine the cumulative distribution function.

a). P(X1.25).

b). P(X2.2).

c). P(-1.1< X1).

d). P(X >0).

a). Now we have to find P(X1.25).

P(X1.25) = 0.9

Therefore, P(X1.25) = 0.9.

Step 2 of 4:

b). Now we have to find P(X2.2).

P(X2.2) = 1

Therefore, P(X2.2) = 1.