The temperature Y at which a thermostatically controlled switch turns on has a probability density function...
Question#3 20 Points Let Y has the density function which is given below: 0.2 -kyS0 f(v) 0.2 + cy 0 0<p 1 otherwise (a) Find the value of c. (b) Find the cumulative distribution function F(y). (c) Use F(y) in part b to find F(-1), F(0), F(1) (d) Find P(0sYs0.5) (e) Find mean and variance of Y d X1 amd 2 aild ate subarea of a fixed size, a reasonable model for (X1, X2) is given by 1 0sx1 S...
Daily total solar radiation for a specified location in Florida in October has a probability density function given by - 4)(6-y), 4 Sy s6, fly) = elsewhere, with measurements in hundreds of calories. Find the expected daily solar radiation for October, in hundreds of calories. E(Y) = hundred calories
having troubles with a (ii) and (c). thanks!
(1) A supplier of kerosene has a weekly demand Y possessing a probability density function given by 0, elsewhere with measurements in hundreds of gallons. The suppliers profit is given by U-10Y-4. (The c.d.f. was calculated in Tutorial Question 4 of week 3) (a) Find the p.d.f. for U i) using the distribution method and) the trans- (b) Use the answer to part (a), to find E(U) (using the p.d.f of U)...
Let X and Y have a joint probability density function f(x, y) = 6(1 − y), 0 ≤ x ≤ y ≤ 1, =0, elsewhere. (a) Find the marginal density function for X and Y . (b) E[X], E[Y ], and E[X − 3Y ]
We were unable to transcribe this imagefunction givě by: . When measured at a location, has a probability density fy(y) 0, elsewhere a) Find the value of k that makes fy(y) a density function. Hint: Does the density have the form of a "known" distribution? b) Determine the mean of Y, E(Y). Hint: a previous problem may be very helpful! c) Using R, simulate 100 values from this distribution and determine the mean of these 100 values. How close is...
Let y be a continuous uniform random variable, Y - Gumbel(B).for ß>0. That is, Y has cumulative density function PIY <y)=Fly)=e for YER. Showing all of your working, find the probability density function of Show that the inverse of the cumulative density function is given by F (y)=u-Bin(–In(y)). for YER. Given realisations {u,, uz,...,Ug} = {0.710,0.119,0.358,0.883,0.504} of a U[0, 1] variable, generate five realisations {y, Y2,..., Ys} of Y-Gumbel(5, 10). Clearly explain your method and any calculations required.
Problem 3. The random variable X has density function f given by y, for 0 ys 0, elsewhere (a) Assuming that θ-0.8, determine K (b) Find Fx(t), the c.d.f. of X (C) Calculate P(0.4 SXS 0.8)
The probability density function of X is given by
0 elsewhere
Find the probability density function of Y = X3
f(r)-(62(1-x)for0 < x < 1
Find the probability that Y is greater than 3.
Let Y have the probability density function f(y) = 2/y3 if y> 1, f(y) = 0 elsewhere.
Two random variables, X and Y, have joint probability density function f ( x , y ) = { c , x < y < x + 1 , 0 < x < 1 0 , o t h e r w i s e Find c value. What's the conditional p.d.f of Y given X = x, i.e., f Y ∣ X = x ( y ) ? Don't forget the support of Y. Find the conditional expectation E [...