a. Probability of getting a project from a financial organization is 2%. It is given that...

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a. Probability of getting a project from a financial organization is 2%. It is given that one person can propose one proposal at a time. Three persons proposed their projects at a time to the organization. The random variable X counts number of granted projects from first two proposals and the random variable Y counts number of granted projects from last two proposals. i. What is the cdf of (X, Y) and marginal cdfs of X, Y? ii. What is correlation coefficient of X and Y? a. Find the density function of Y = BX where a > 0, ß> 0 if X is exponentially distributed with mean μ-1. b. Find the density function of Y = ex if X is normally distributed with mean u and standard deviation o. The joint probability functions of the rv (X, Y) is f(x,y)={ [k(x+y+3xy), if1<x<2, 1<y<2 otherwise. 0, (i). Find the point (x, My) where x is median of X and μy is median of Y. (ii). Compute Corr (X, Y). Stopping distance of a car. x =speed [mph], y = stopping distance [ft]. x 30 40 50 60 70 75 80 85 90 y 160 240 350 450 600 650 700 800 950 Find and graph the sample regression line of y on x and the given data as points on the same axes and also find y at x = 65. i. Explain the degree of freedom with example. ii. Explain confidence interval. Write the steps to find CI of mean and variance Explain both side alternative of variance and testing of hypothesis of variance. iii. a. Probability of getting a project from a financial organization is 2%. It is given that one person can propose one proposal at a time. Three persons proposed their projects at a time to the organization. The random variable X counts number of granted projects from first two proposals and the random variable Y counts number of granted projects from last two proposals. i. What is the cdf of (X, Y) and marginal cdfs of X, Y? ii. What is correlation coefficient of X and Y? a. Find the density function of Y = BX where a > 0, ß> 0 if X is exponentially distributed with mean μ-1. b. Find the density function of Y = ex if X is normally distributed with mean u and standard deviation o. The joint probability functions of the rv (X, Y) is f(x,y)={ [k(x+y+3xy), if1<x<2, 1<y<2 otherwise. 0, (i). Find the point (x, My) where x is median of X and μy is median of Y. (ii). Compute Corr (X, Y). Stopping distance of a car. x =speed [mph], y = stopping distance [ft]. x 30 40 50 60 70 75 80 85 90 y 160 240 350 450 600 650 700 800 950 Find and graph the sample regression line of y on x and the given data as points on the same axes and also find y at x = 65. i. Explain the degree of freedom with example. ii. Explain confidence interval. Write the steps to find CI of mean and variance Explain both side alternative of variance and testing of hypothesis of variance. iii.

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a i The cumulative distribution function CDF of X Y can be calculated as follows CDFX Y PX x Y y To find the joint CDF we need to consider all possible combinations of X Y and calculate their probabil... View the full answer