# probability mass function

• Jan 21st 2009, 05:13 PM
Sally_Math
probability mass function
Suppose a random variable X has a cumulative distribution function given by
F(a) = {0 for a<0, 1/2 for 0<=a<1, 3/5 for 1<=a<2, 4/5 for 2<=a<3,
9/10 for 3<=a<3.5, 1 for 3.5<=a.
a. Find the probability mass function for X.
b. Find the probability that a given observation of the value of X is greater than or equal to 1.5.
(Bow)(Bow)
• Jan 22nd 2009, 02:06 AM
mr fantastic
Quote:

Originally Posted by Sally_Math
Suppose a random variable X has a cumulative distribution function given by
F(a) = {0 for a<0, 1/2 for 0<=a<1, 3/5 for 1<=a<2, 4/5 for 2<=a<3,
9/10 for 3<=a<3.5, 1 for 3.5<=a.
a. Find the probability mass function for X.
b. Find the probability that a given observation of the value of X is greater than or equal to 1.5.
(Bow)(Bow)

(a) Since X appears continuous rather than discrete, the term would be probability density function ..... Use f(a) = dF/da.

(b) $\Pr(X \geq 1.5) = 1 - \Pr(X <1.5) = 1 - F(1.5)$