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3. Let the probability density function of a continuous random variable X be defined f(x) = {x²/9 [x²/9 if 0≤x≤3 otherwise Find E(X) and Var(X).

3. Let the probability density function of a continuous random variable X be defined f(x) = {x²/9 [x²/9 if 0≤x≤3 otherwise Find E(X) and Var(X).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I need help with question #3 please Homework review
2. L 3. ] Suppose the c.d.f. of a random variable X is defined as if x < 0 if 0 < x < 1 if 1 ≤ x < 2 if x ≥ 2 Find each of the following probabilities. (a) P(X= 2) F(x) = Find the c.d.f of X. 0 x²/4 2x/5 1 Find E(X) and Var(X). (b) P(X ≥ 1) Suppose the p.d.f. of a random variable X is defined as x²/63 if 3 ≤x≤6 otherwise (c) P(1/2 < X ≤ 2) f(x) = = {x²/63 Let the probability density function of a continuous random variable X be defined a f(x) = {x²/9 if 0 ≤ x ≤ 3 otherwise 4. In a school, the height of all male students has an approximately normal distribution with the mean of 178 cm and the standard deviation of 3 cm. (a) 3] When a male student in the school is randomly surveyed, what is probability that he is below 180 cm? (b) When 16 male students in the school are randomly surveyed, what is the probability that their average height is above 179 cm? 5. In a supermarket, there are chicken eggs and duck eggs. Assume the weight of each type of eggs is normally distributed. The chicken eggs have a mean of 50 grams and a standard deviation of 3 grams; the duck eggs have a mean of 60 grams and a standard deviation of 5 grams. When a chicken egg and a duck egg are randomly chosen, estimate the probability that the duck egg weights more than a chicken egg. (b) When two chicken eggs and three duck eggs are randomly chosen, estimate the probability that their total weight is between 275 and 300 grams.
Transcribed Image Text:2. L 3. ] Suppose the c.d.f. of a random variable X is defined as if x < 0 if 0 < x < 1 if 1 ≤ x < 2 if x ≥ 2 Find each of the following probabilities. (a) P(X= 2) F(x) = Find the c.d.f of X. 0 x²/4 2x/5 1 Find E(X) and Var(X). (b) P(X ≥ 1) Suppose the p.d.f. of a random variable X is defined as x²/63 if 3 ≤x≤6 otherwise (c) P(1/2 < X ≤ 2) f(x) = = {x²/63 Let the probability density function of a continuous random variable X be defined a f(x) = {x²/9 if 0 ≤ x ≤ 3 otherwise 4. In a school, the height of all male students has an approximately normal distribution with the mean of 178 cm and the standard deviation of 3 cm. (a) 3] When a male student in the school is randomly surveyed, what is probability that he is below 180 cm? (b) When 16 male students in the school are randomly surveyed, what is the probability that their average height is above 179 cm? 5. In a supermarket, there are chicken eggs and duck eggs. Assume the weight of each type of eggs is normally distributed. The chicken eggs have a mean of 50 grams and a standard deviation of 3 grams; the duck eggs have a mean of 60 grams and a standard deviation of 5 grams. When a chicken egg and a duck egg are randomly chosen, estimate the probability that the duck egg weights more than a chicken egg. (b) When two chicken eggs and three duck eggs are randomly chosen, estimate the probability that their total weight is between 275 and 300 grams.
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