Probability & Statistics Joint Probability Distribution - Statistics Assignment Help

Assignment Task:

Task:

1. (a) If the joint pdf of (X,Y) is given by f(x,y) =3xy(x+y) , 0≤x , y≤1 ; find the value of E{E(Y/X)} , E(Y) .
(b) The following table represents the joint probability distribution of the discrete random variable (X, Y), Find all the marginal and conditional distributions:

Y X

1 2 3
1 1/12 1/6 0
2 0 1/9 1/5
3 1/18 1/4 2/15

2. If the density function of a random variable X is given by f(x) =kx(1-x) , 0≤x≤1 , Find the A.M. , H.M. , Median , Mode , S.D. , M.D. , about the mean , β1 and β2 .

3. A certain drug was administered to 500 people out of a total of 800 included in a sample to test its efficiency against Typhoid , the result are given below :

Typhoid No Typhoid Total
Drug 200 300 500
No Drug 280 20 300
Total 480 320 800
On the basis of data, can we say that drug is effective in preventing Typhoid?

4. Use the method of least square to fit the curve : y=c0 /x +c1√x to the following table of values :

x 0.1 0.2 0.4 0.5 1 2
y 21 11 7 6 5 6

5. Find the regression lines of the following data :

x 5 7 8 10 11 13 16
y 33 30 28 20 18 16 9

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