(e) Are X and Y dependent or independent? Explain why.

(f) Find means μX and μY.

(g) Find variances,
.
(h) Find covariance and correlation coefficient,

3. The joint probability density function for random variables X and Y is:

(a) Sketch fXY.

(b) Find the marginal distributions of X and Y.

(c) Find the conditional distributions of X|Y and Y |X.

(d) Find

(e) Are X and Y dependent or independent? Explain why.

(f) Find means, μX and μY.

(g) Find variances

.
(h) Find covariance and correlation coefficient,

4. The times that a cashier spends processing each person's transaction are independent and identically distributed random variables with a mean of 1.5 minutes and standard deviation of 1 minute.

(a) What is the approximate probability that the orders of 100 people can be processed in less than 2 hours?

(b) Find the number of customers, n, such that the probability that the orders of all n customers can be processed in less than 2 hours is approximately 0.9.

Moment Generating Function, Marginal and Conditional Distributions and Probability Density Functions are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

... included in the integration) The marginal densities is ... 2y , 0 < y < 1 The conditional densities of ... Y|X=x ~ Bin(x,p) Hence the Moment generating function of X ...

... MT2131 i) The moment generating function of X is the following ... 1 E( X ) = λ The second moment (which is E ... be taken outside the expected value function: E ( et ...

... mass functions and cumulative distribution functions are investigated ... (i) Find the marginal distributions of X ... MX (t), the moment generating function (mgf) of X ...

... the strategies that can be used to create a product ... 2SLS is equivalent to Generalized Method of Moments (GMM).7 ... form for the marginal cost function, such that c ...

... The moment you ease up you have lost the battle ... in order that it may continue to create a customer ... This ability to change comes from the function of innovation ...

... in a previously unexplored area can generate huge potential ... to us from a simple density function curve. ... are illustrated below (ignore for the moment that the ...

... a firm's debt/assets ratio as a function of the ... cash flow after depreciation, the reinvestment generated in the ... We leave in abeyance for the moment which root ...

... Even at such moments of maximum collec- tivity, the ... This was the moment of greatest tension between the ... structures and procedures that unions create are often ...

... resources left to train teachers to create and conduct ... They cannot inform the moment-to-moment, day-to ...functions, often at the expense of the learning function. ...

... efﬁciency and effectiveness in order to create loyal customers ... 3. Both companies are facing the same demand function. ... I feel at this moment more anxiety for ...