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- ACC Vly, calculate the average value of the Y random variable defined as Y = X A 2 + 2 and the probability P (Y = 2). E[Y] = 2.7, P (Y- 2) = 0.5 The random variable X is defined as a random variable that can take integer values in the range -3Given the probability density function f(x)=1/3 over the interval [3,6] find the expected value, the mean, the variance and the standard deviation.Choose between a b and c for mean, medium, and modeCompute the mean of Y Compute the mean of X. Compute the variance of X Compute the variance of Y Compute the covariance of X and Y Compute the correlation of X and Y Joint Distribution of Weather Conditions and Commuting Times No Rain (X1) 0.28 0.05 0.33 Long commute (Y=0) Short commute (Y=1) Total Rain (X=0) 0.38 0.29 0.67 E(M)= 0.34 (Round your response to two decimal places) E(X)=0.33 (Round your response to two decimal places) = 2211 (Round your response to four decimal places) 2244 (Round your response to four decimal places) comp ®x*[ ] (Round your response to four decimal places) Total 0.66 0.34 1.00Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean u = 29.6 kilograms and standard deviation o = 5.0 kilograms. Let x be the weight of a fawn in kilograms. The Standard Normal Distribution u = 0, o = 1) -2 3 68% of area 95% of area 99.7% of area For parts (a), (b), and (c), convert the x intervals to z intervals. (For each answer, enter a number. Round your answers to two decimal places.) (a) x< 30 1x (b) 19 < x (Fill in the blank. A blank is represented by ) (c) 32 < x < 35 (Fill in the blanks. A blank is represented by There are two answer blanks.) first blank second blank For parts (d), (e), and (f), convert the z intervals to x intervals. (For each answer, enter a number. Round your answers to one decimal place.) (d) -2.17 < z (Fill in the blank. A blank is represented by ) (e) z< 1.28 (f) -1.99 < z< 1.44 (Fill in the blanks. A blank is represented by There are two answer blanks.) first blank second blank (g) If a fawn weighs 14…Given the probability density function f(x)=14f(x)=14 over the interval [2,6][2,6], find the expected value, the mean, the variance and the standard deviation.Expected value: Mean: Variance: Standard Deviation:If a dealer's profit, in units of $3000, on a new automobile can be looked upon as a random variable X having the density function below, find the average profit per automobile. f(x) = 1 (7-x), 0Random variable X has a standard normal distribution. Find the PDF of the random variable Y, where: (a) Y = 3X - 1. (b) Y = 3X² – 1.Given the probability density function f(x)=13f(x)=13 over the interval [4,7][4,7], find the expected value, the mean, the variance and the standard deviation.Expected value: Mean: Variance: Standard Deviation:Let X be the random variable of the normal distribution with mean (u) and standard .deviation (o) If P(u < x < u+4) = 0.37900 =then standard deviation (ơ)Given the probability density function f(x)=14f(x)=14 over the interval [3,7][3,7], find the expected value, the mean, the variance and the standard deviation.Expected value: Mean: Variance: Standard Deviation:Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean u = 4.3 and standard deviation a = 0.5. The Standard Normal Distribution (-0, 0-1) -3 -2 -1 0 68% of area 95% of area 99.7% of area 2 3 Z (a) Convert the x interval, 4.5 < (d) Convert the z interval, z < -1.44, to an x interval. (Round your answer to one decimal place.) x < (e) Convert the z interval, 1.28SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON