# Probability and random random varible question

• May 15th 2010, 08:59 AM
artikiller
Probability and random random varible question
Hi im not to sure how to show and work out these two questions? It would solve a great deal of problems if someone could help. Cheers

Question 1) Recent astronomical observations indicate that, of the 20 stars closest to our sun,
about half are accompanied by an orbiting planet at least the size of Jupiter.
Assume that the proportion of such stars in the galaxy is 0.5. There is a group of 20 stars.

Show that there is approximately an 8% chance of there being more than 13 or less
than 6 with such a planetary system in such a group.

also

Question 2) Consider three random variables
X, Y and Z which respectively represent the exam, skills test total and assignment scores (out of 100%) of a randomly chosen student.
Suppose that past experience suggests the following properties of these assessment items
(each out of 100%):

E(X) = 55, sd(X) = 12
E(Y) = 70, sd(Y) = 16
E(Z) = 67, sd(Z) = 10
.

Find the distribution parameters,
E(T) and Var(T), for the total mark, T=0.5X+0.32Y+0.18Z.
• May 15th 2010, 08:53 PM
rubic
Q1) binomial dist (20,0.5)
P(x>13) + P(x<6) = 0.08

binomial dist is discrete
P(x>13) = 1 - P(x<=13)
P(x<6) = P(x<=5)

use neave's table

P(x>13) + P(x<6) = 1-0.9423 + 0.0207 = 0.0784, which is approx 8%

Q2)
T=0.5X+0.32Y+0.18Z, E(T) and Var(T)
E(T) = 0.5*55+0.32*70+0.18*67 = 61.96
Var(T)
= (0.5^2)*(12^2)+(0.32^2)*(16^2)+(0.18^2)*(10^2)=
65.4544

hope it helps