"1. knowing only that logo5=x and log 67=y, Find each . (3 pts) logo 35 p)...
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(1 point) Rewrite the expression below as a single logarithm. 3 logo x – 5 logo y + 5 logo z = logo (1 point) Rewrite the expression 4 log2 x – 2 log2 y + 5 log2 z as log2 A for A= (1 point) Rewrite the expression logio yoyo = 10810x+ logo + logo z (1 point) Expand using the properties of the logarithm. log: txan log; x+ logz y- log: 2 (1 point) Find the...
6. Find the value of y a. log, 3) = y b. log, = y log (1125) = y d. 10° = y 15 =y 1 e 50 9. 200 7. Given the function and t f(0) = 2 g(x) = 5* Draw the 2 function. Which one grows faster with increasing & 8. Plot f(x) = log, (x) = y log2 (L) =y and g(x) =
1. Rewrite the following as a single logarithm: log p- (log 9-3 log y (2 marks) 2 2. Given a3x = 2 and a®) = 9, then determine an expression that represents the value of log, 18 . (2 marks) 3. A student's work to simplify a logarithmic expression as shown below, where a >1 Step 1 Step 2 2 log, ** – 3 log, x? +4log, x' log, ** – log, x° + log, x'? x Step 3 log....
Question 1. (15 pts) Given f(x,
y) = 3x 2 + y 3 . (a) Find the gradient of f. (b) Find the
directional derivative of f at P0 = (3, 2) in the direction of u =
(5/13)i + (12/13)j.
Question 1. (15 pts) Given f(L,y) = 3x2 +y?. (a) Find the gradient of f. (b) Find the directional derivative off at P =(3,2) in the direction of u=(5/13)i + (12/13)j.
tion? (2) Calculate E(X), E(X2), and Var(X). (3) Calculate F(a) P(X s a) for a (0, 1]. (4) Let Y =-log X. Calculate F(y)-P(Y v) for u 20. Calculate the density of Y.
tion? (2) Calculate E(X), E(X2), and Var(X). (3) Calculate F(a) P(X s a) for a (0, 1]. (4) Let Y =-log X. Calculate F(y)-P(Y v) for u 20. Calculate the density of Y.
12. The Gumbel distribution is the distribution of log X with X Expo(1). Find the CDF of the Gumbel distribution. 13. Suppose X ~ U[0, 1] and Y = - In(X) (so Y > 0). Find the p.d.f. of Y
12. The Gumbel distribution is the distribution of log X with X Expo(1). Find the CDF of the Gumbel distribution. 13. Suppose X ~ U[0, 1] and Y = - In(X) (so Y > 0). Find the p.d.f. of Y
Knowing that events X and Y are statistically independent, find the value of A Y=0 Y=1 Marginal probability of X X=0 0.5+A 0.3-A X=1 0.1 0.1 Marginal probability of Y 1
Let X and Y have the joint pdf fXY(x,y) = 24xy^3, 0<y<x<1. Find P(X>2/3, Y<1/3) Find P(X<2Y)
Write the expression as a single logarithm. Express powers as factors. logo - log ex? log 6VX-log 6x2=0 (Type an exact answer. Use integers or fractions for any numbers in the expression.) Writing log aP - log aq +4 logar as a single logarithm results in which of the following expressions? Choose the correct answer below. log (p - q +4r) o 109.(4) o log. ( 10 10g, (+4) aboo Write the following expression as a sum and/or difference of...
I. The random variables X,, where P(success) = P(X = 1) = p = 1-P(X = 0) for1,2,..., represent a series of independent Bernoulli trials. Let the random variable Y be the trial number on which the first success is achieved (a) Explain why the probability mass function of Y is f(y) = pqy-1, y = 12. where q 1- p. State the distribution of Y. 2 part of your answer you should verify this is a marimum likelihood estima-...