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If the results of 100 observations, which had a standard deviation of 0.5, were gathered randomly into groups of 10 and the mean of each group recorded, what would you expect to be the value of the standard deviation of the group of means thus produced?
If %10 of the rivets produced by a machine are defective, find the probability that out of 5 randomly chosen rivets. i) one or more will be defective. ii) at most two will be defective.
The distribution of IQ for 12-year-olds is known to be normal with mean 100 and standard deviation 16. What must then be the probability for a 12-year-old to have an IQ of 124 or more? What is the probability for a 12-year-old to have an IQ of 84 or less?
For the random variable Xwith the following probability density function ⎩⎨⎧<≥=−0x;00x;e2)x(fx2, find i) )1|X|(P>μ− ii) Use Chebyshev’s inequality to obtain an upper bound on ]1|X|[P>μ− and compare with the result in (i).
Let )X,,X,X(n21K be a random sample from a distribution with density function ⎩⎨⎧α≤≤α=αotherwise;0x0;/1),x(f Obtain the maximum likelihood estimator of θ.
Let Y,X have joint pdf ⎩⎨⎧≤≤≤≤=otherwise;01y0,1x0;4)y,x(fy,x Find )y/x(f),y(f),x(fY/XYX and )x/y(fX/Y. Also, find )yY|X(E= and )xX|Y(E=.
Let n21X,,X,XK be a random sample with m)X(Ei= and 2i)X(Varσ= for all n,,2,1iK=. Show that )XX(1n1Sn1ii2∑=−−= is an unbiased estimator of 2σ.
how many grains of rice would it take to cover florida one meter deep
find the volume and lateral area of a truncated right square prism whose base edge is 4ft., and whose lateral edges measure 6ft., 7ft., 9ft., and 10ft.
Solve the following differential equations
(i) x^2 p + y^2 q = ( x+ y) z .
(ii) (root of p) − (root of q) + 3x = 0
(i) x^2 p + y^2 q = ( x+ y) z .
(ii) (root of p) − (root of q) + 3x = 0
