Math Answers

6 observations on (X, Y)yielded the following data:

rxi = so, rvi = rso, rxivi = 1000.

rxf =200, rv,2 =5642.

i) Determine the correlation coefficient between X and Y.
ii) Given X =IO, what will be the predicated value ofY?

iii) Given Y =IS, predict X.

JfX is a random variable with E(X) = 3 and E(X2




= 16, find a lower bound for the



probability P[-2 < X < 8).

) For a Poisson distributed random variable X, P(X = 4) = P(X = 5). What is the mean and variance of the distribution?

Let (X, Y) have the following joint p.d.f.


f(x,y) = {6xy ,0 s x s l,O s y s l
0, otherwise

Find P(2Y + X ;:>: I).

Xis a random variable taking values O and I with respective probabilities q and p. A
sample X1,X2, •••• ,X. of size n is taken from the distribution. If r = I,x,, shows that
isl
the bias of the estimator tends to zero as n tends to infinity

For the following frequency table obtain the relative frequencies and the cumulative frequencies of the 'more than' type.

Distribution of250 lamp bulbs by life (in hours)

Li& {fn hours)

499.5 - 649.5 Freguenc�

5
649.5 - 799.5 20
799.5 - 949.5 40
949.5 - 1099.5 81
1099.5 - 1249.5 57
1249.5 - 1399.5 34
1399.5 - 1549.5 13
Total 250

Also determine the number of bulbs having a life of 1249.5 hours or less.

Ken just bought a house. He made a $15000 down payment and financed the balance with a 30 year home mortgage loan will an annual interest rate of 6.3% compounded monthly. His monthly mortgage payment is $938. What was the selling price of the house?

Given tan⁡u=-1/3 and sin⁡〖u<0,〗 find sin⁡(u/2). (Assume 0≤u<2π.)



-√((10+3√10)/20) b. √((10-3√10)/20) c. √((10+3√10)/20)

d. -√((10-3√10)/20) e. None of these

Given tan⁡θ=3/4 and sin⁡〖θ)]<0, find tan⁡2θ.


a. 1/3 b. √5/3 c. 5/9 d. 24/7 e. None of these

Simplify: cos⁡(5π+x)


a. cos⁡x b.〖 sin〗⁡x c. -sin⁡x d. -cos⁡x e. None of these