For 25 army personnels, line of regression of weight of kidneys (Y) on weight of heart (x) is Y = .0 399X + .6 934 and the line of regression of weight of heart on weight of kidney is X − .1 212Y + .2 461= .0 Find the correlation coefficient between X and Y and their mean values.
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Let X be a binomial variate with n =100, p = .1.0 Find the approximate value of P (10 ≤ X ≤12) using:
(i) normal distribution
(ii)poisson distribution
[You may like to use the following values.
P(Z ≤ 67.0 ) = .0 7486, P(Z ≤ 0.33 ) = .0 6293, P(Z ≤ 0 ) = ]5.0
Let X1, X2,,,,,,, Xn , , , be independently and identically distributed b ,(1,p) random variables. Obtain a confidence internal for p using Chebychev’s inequality.
If the moment generating function (m.g.f.) of a random variable X is Mx(t ) exp (3t 32t2 ). Find mean and standard derivation of X and also compute P(x < ).3
For a distribution, the mean is 10, variance is 16, the skewness sk4 is +1 and kurtosis b2 is 4. Obtain the first four moments about the origin i.e. zero. Comment upon the nature of the distribution.
For normal distribution with mean zero and variance σ2 show that:
The probability density function of a random variable X is f (x) = C | x |; Find C, and the value of x0 such that where F isthe CDF.
For the given bivariate probability distribution of X and Y :
for x = 0,1,2,3 and y = 0,1.
Find:
(i) P(X ≤ ,1 Y = )1
(ii) P(X ≤ )1
(iii) P(Y > )0 and
(iv) P(Y = 1| X =3 )