Question

They have available 10 boxes of honey, 4 boxes of el Duende, 6 boxes of bimbos, 15 boxes of oreos . Each sells for 6$.

a) Define your random variable.

b) Determine the probability distribution and parameters for the random variable.

c)Suppose that, after two hours, ten boxes of them have been purchased. Determine the cumulative distribution function for the number of honey purchased.

d)Draw the probability distribution function for the number of honey purchased.

Some body please hurry

Answer 1

a.

random variable X : type of box they sell

it can be : { honey , el Duende, bimbos, oreos }

b.

parameter :

total boxes = 10+4+6+15 = 35

distribution :

P(X) = no. of boxes of X / total boxes

P(honey) = 10/35

P(el Duende) = 4/35

P(bimbos) = 6/35

P(oreos) = 15/35

c.

x = no. of honey purchased out of 10

x can be : 0 to 10

no. of honey boxes = 10

no. of non honey boxes = 35-10 = 25

P(x honey purchased out of 10) = (select x honey out of 10)*(select (10-x) non honey out of 25) / (select 10 boxes from 35 boxes)

= 10Cx * 25C(10-x) / (35C10)

= 10Cx * 25C(10-x) / 183579396

cummulative probability distribution = P(x<=X) = P(0) + P(1) + ...+P(X)

P(x<=X) = ( 10C0 * 25C(10) / 183579396 ) + (10C1 * 25C(9) / 183579396 ) + .....(10CX * 25C(10-X) / 183579396 )

d.

probability distribution function for the number of honey purchased :

P(x honey purchased out of 10) = (select x honey out of 10)*(select (10-x) non honey out of 25) / (select 10 boxes from 35 boxes)

= 10Cx * 25C(10-x) / 35C10

= 10Cx * 25C(10-x) / 183579396

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