Question

Consider the following cumulative probability
distribution.

x |
0 | 1 | 2 | 3 | 4 | 5 |

P(X ≤ x) |
0.10 | 0.29 | 0.48 | 0.68 | 0.84 | 1 |

**a.** Calculate *P*(*X* ≤ 2).
**(Round your answer to 2 decimal places.)**

**b.** Calculate *P*(*X* = 2).
**(Round your answer to 2 decimal places.)**

**c.** Calculate *P*(2 ≤ *X* ≤ 4).
**(Round your answer to 2 decimal places.)**

Answer #1

We calculate P(X = x) from cumulative frequency P(X <= x) as

P( X = x) = P( X <= x) - P( X <= x-1)

For example,

P(X =2 ) = P( X <=2 ) - P( X <= 1)

= 0.48 - 0.29

= 0.19

X | 0 | 1 | 2 | 3 | 4 | 5 |

P(X <= x) | 0.10 | 0.29 | 0.48 | 0.68 | 0.84 | 1 |

P(X = x) | 0.10 | 0.19 | 0.19 | 0.20 | 0.16 | 0.16 |

a)

P( X <= 2) = P (X = 0) + P (X = 1) + P (X = 2)

= 0.10 + 0.19 + 0.19

= **0.48**

b)

P( X = 2) = **0.19**

c)

P( 2 <= X <= 4) = P( X = 2) + P (X = 3) + P (X = 4)

= 0.19 + 0.20 + 0.16

= **0.55**

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