The number of cokes X that an individual drinks at a party e

The number of cokes (X) that an individual drinks at a party event has the following probability mass function:

X= 0, 1, 2, 3, 4, 5

Probability= 0..3, 0.2, 0.2, 0.1, 0.1, 0.1

a) Find the expected number of cokes an individual drinks at a party.

b) Find the probability that an individual drinks no more than 2 cokes.

c) Find P(1.2<X<equalto 4)

d) Find F(2.05), where F is the cumulative probability density function.

Solution

Let X be a ranbom variable that the number of cokes (X) that an individual drinks at a party event.

the expected number of cokes an individual drinks at a party that is we have to find mean.

mean = x*p(x)

mean = 1.8

  the expected number of cokes an individual drinks at a party is 1.8

the probability that an individual drinks no more than 2 cokes.

That is P(X=0 or X =1)

P(no more than 2 cokes) = P(X=0)+P(X=1)

= 0.3 + 0.2 = 0.5

Find P(1.2<X<equalto 4) = P(X=2) + P(X=3)+P(X=4) = 0.2 + 0.1 + 0.1 = 0.4

P(1.2<X<equalto 4) = P(1.2 < X <=4) = 0.4

Find F(2.05), where F is the cumulative probability density function.

F(x) = P(X x)

F(2.05) = P(X 2.05)

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

= 0.3 + 0.2 + 0.2 = 0.7