Statistics and Probability Answers

In a cribbage game with 2 people, each player is dealt 6 cards to start a round. How many 6- card hands are possible?

According to Nielsen Media Research, approximately 67% of all U.S. households with television have cable TV. Seventy-four percent of all U.S. households with television have two or more TV sets. Suppose 55% of all U.S. households with television have cable TV and two or more TV sets. A U.S. household with television is randomly selected.

a. What is the probability that the household has cable TV or two or more TV sets?

b. What is the probability that the household has cable TV or two or more TV sets but not both?

c. What is the probability that the household has neither cable TV nor

A box contains 20 coloured balls. There are 5 balls each with the following colours: blue, red, yellow and green. The 5 balls of each colour are numbered from one to five. 4 balls are randomly selected at once.

a)How many ways can 4 balls of the same colour be selected?

b)How many ways can exactly 2 of the 4 balls selected have the same colour?

c)How many ways can the 4 balls selected consist of 2 balls each of two different numbers?

A division-wide aptitude test in Mathematics was conducted to 1000 pupils. The mean of the rest is 58 and the standard deviation is 12. The scores also approximate the normal distribution. What is the minimum scores to belong to the upper 10% is the group?

The top 5 students are getting awards for the highest marks in Grade 11. There are 2 boys 

      and 3 girls. For a picture they are randomly seated along a bench in the gym.    

What is the probability that the students are seated in order of age 

             (assuming no birthdays  are the same)

For the given distribution:

P(X=x) = 2/3(1/3)^x ; x= 0,1,2,....., find moment generating function, mean and variance of X

State whether the following statements are true or false. Give a short proof or a counter  example in support of your answers:

(a) Poisson distribution is a limiting case of binomial distribution for n→∞, p→1 and np→∞.

(b) For two independent events A and B, if P(A) = 2.0 and P(B) = ,4.0 then (A∩ B) = .6.0

(c) If H₀: P ≤ 6.0 and X ~ B(n, p) n -known and p unknown and H₁ :µ = µ₀ where 

X ~ N (µ,σ²)σ² unknown, then H₀

and H₁ are simple null hypothesis. 

(d) Frequency density of a class for any distribution is the ration of total frequency to  class width. 

(e) If X and Y are independent r.v.s with M_x(t) and M_Y(t) as their m.gf's respectively, then M_X+Y (t) = M_X (t) M_Y(t).

Random samples of 400 men and 600 women were asked whether they would like

to have flyover near their residence. 200 men and 325 women were in favor of the

proposal. Test the hypothesis that proportions of men and women in favor of the

proposal are same against that they are not, at 5% l.o.s.

Let X₁,X₂,.....,X_n be random sample of size n from a distribution with probability 

density function 

f(X; ,0)={ θX^(θ-1), 0<X<1, θ>0; 0, elsewhere

Obtain a maximum likeyhood estimator of θ.

For normal distribution with mean zero and variance σ² show that:

E(|x|)= [√(2/π)]σ.