2.5 Solve the below problem: Y has a density function - y),0 < y s 2 |(2 – fy) = 0, elsewhere Find the mean and standard deviation of Y.

inclue the variance

endent. 3.60 The joint probability density function of the ran- dom variables X, Y, and Z is ry=", 0 }, 2 < Z < 3); (d) P(0 < Z < 2 | X = , Y = }). 75°F Mostly cloudy

Im having trouble to do the working. Kindly assist me

Please don't provide handwrittin solution...

Thank you.

EX#1: Let the continuous random variable X denote the current measured in a wire in milliamperes. Assume that the range of X is [4.9,5.1] mA, and assume that the probability density function of X is f (x) = 5 for 4.9 < x < 5.1. Calculate the mean, variance and standard deviation.

7 & 15.

5. Find the average value of f(x) == on [e¹, e5]. X

Suppose that the graph below represents the density function for the times (in weeks) that Canadians will need to wait before receiving a COVID-19 vaccine, starting today, as predicted by the Canadian goverment. y = p(t) Wait Time t (weeks) 3 (a) Given that p is a density function, what numerical value should be placed in the pink box? The value in the pink box is mumber units (b) For each question below, please write your answer into the box. You do not need to explain your reasoning. i. What fraction of Canadians will receive their vaccine within 2 weeks from today? (Please state your answer in the form of a fraction.). ii. What is the median wait time? iii. Without doing any calculations, how do you expect the mean wait time to compare with the median? (Please fill in the blank below using the words "greater than", "less than", or "equal to".) weeks I expect the mean wait time to be the median. iv. According to this model, what is the longest possible time that a Canadian might need…