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^ d z i Z p x s X t w H Ä. Function p(y 1;y 2), then 1 0 p(y 1;y 2) 1 for all y 1, y 2 2 P y1;y2 p(y 1;y 2) = 1, where the sum is over all values (y 1;y 2) that are assigned nonzero probabilities Al Nosedal University of Toronto STA 256 Statistics and Probability I. ^ v%&1/ @ A G \ _ ^ W Z 8 r M S T K ( ^&.

7 8 ) &. 2 Setting P/Y and C/Y P/Y stands for payments per year, and C/Y for compounding periods per year For BA II Plus, the defaults for P/Y and C/Y are 12 That is, 12 payments per year and 12 compounding periods per year To set both P/Y and C/Y to be the SAME number such as 1 (one payment per year and annual compounding) follow this sequence 1. # y u t ¹.

S z è. P Y (y) I In words rst restrict sample space to pairs (x;y) with given y value Then divide the original mass function by p Y (y) to obtain a probability mass function on the restricted space I We do something similar when X and Y are continuous random variables In that case we write f f(x;y) XjY (xjy) = f Y (y) I Often useful to. { $9$ 0\64/ 6SULQJ )UDPHZRUN n j / 	.

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Y ) 5 B G #. G M ` ü. Solve for y y/(pq)=y/(pq) Multiply both sides of the equation by Multiply and Move all terms containing to the left side of the equation Tap for more steps Subtract from both sides of the equation To write as a fraction with a common denominator, multiply by.

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% % ;. This is a set of very simple calculators that generate pvalues from various test scores (ie, t test, chisquare, etc) Pvalue from Z score Pvalue from t score Pvalue from chisquare score Pvalue from Fratio score Pvalue from Pearson (r) score Pvalue from Tukey q (studentized range distribution) score Critical Values Calculators. X, zero elsewhere a) What must the value of C be so that f X, Y (x, y) is a valid joint pdf?b) Find P (X Y <.

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Doesn’t give us any information about the other(s) That is, p(XjY = y) = p(X) for all y This means that the joint factorizes as the product of the marginals p(X, Y) = p(XjY)p(Y) = p(X)p(Y) Examples of rv’s that are not independent include Whether it rains and whether you go to the beach A person’s height and a person’s sex. 6655 of the Internal Revenue Code by adding new subsection (e)(5) This subsection provides that any dividend that is received. \$ ^ W Z 8 S Ú.

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4 19 Suppose that X and Y hare independent random variables, gand are two functions, and E(g(X)) and E(h(X)) existShow EgXhY EgX EhY(( )()) (( )) (())= The following table gives the joint probability distribution between employment status and college graduation among those either employed or looking for work. ¡1 ¿“§‡√ ’¬π∑ ’. S v ^ X s æ.

EC02 Spring 06 HW7 Solutions March 11, 06 3 Problem 421 Solution In this problem, it is helpful to label points with nonzero probability on the X,Y plane. U ~ r Ã. P P O O ¦.

9 0( % 1 ;. Õ∫ «‘∑¬“»“ µ√ å. F = P (1 i) n or single payment interest table factors can be used to solve for unknown i or n Example A $100 investment now in an account that pays compound interest annually will be worth $250 at a point exactly 31 years from now What annual interest rate does this account pay?.

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