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4. Let the pdf of a continuous random variable X be defined as (x+3)/6 if-3≤x<0 if 0≤x≤1 otherwise (a) (b) f(x)= (1-x)/2 Find the cdf of X. Find E(X) and Var(X).

4. Let the pdf of a continuous random variable X be defined as (x+3)/6 if-3≤x<0 if 0≤x≤1 otherwise (a) (b) f(x)= (1-x)/2 Find the cdf of X. 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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Homework review please help Question #4
1. (a) (b) 2. Peter usually goes to the river in his neighborhood to catch fishes over the weekends. Based on his experience in the past, he could catch 3 fishes per hour on average. Assume the number of caught fishes has a Poisson distribution. What is the probability that he catches at least 2 fishes in a given 30 minutes? Use exponential distribution to find the probability that no fishes are caught in a given 20 minutes. (a) (b) When a hand of 5 cards is dealt from a standard deck of 52 cards, what is the probability that a full-house is obtained? (ex: aaabb) When a hand of 5 cards is dealt to each of three players, what is the probability that no one receive Aces? (a) 3. Consider a special six sided die with one blue face, two green faces and three red faces. When the die is rolled 3 times, if it's known that no blue face is obtained, what is the probability that more red faces than green faces are obtained? (b) [ When the die is rolled 30 times, what is the probability of getting green faces between 11 and 13 times? 4. Let the pdf of a continuous random variable X be defined as f(x)= if-3 ≤ x < 0 if 0 ≤ x ≤ 1 otherwise (a) (b) ((x+3)/6 (1-x)/2 .0 Find the cdf of X. Find E(X) and Var(X). 5. In a supermarket, the weights of apples and pears have approximately normal distributions. The weight of apples has the mean 150 g and the standard deviation of 15 g; the weight of pears has the mean of 200 g and the standard deviation of 25 g. (a) When a pear and two apples are randomly chosen, what is the probability that their total weight exceeds 540 g? (b) Assume apples cost 0.6 cent per gram and pears cost 0.5 cents per gram. When an apple and a pear are randomly chosen, what is the probability that the apple costs more than the pear? In a college, 400 students are graduating this semester. According to the school policy, each student is allowed to invite up to 3 people to the graduation ceremony. Based on the experience from the past, the school estimates the probabilities that a student will bring 0, 1, 2, and 3 people are 10%, 40%, 30% and 20% respectively. Assume the estimation is correct and the college prepares 680 chairs for the invited people, what is the probability that every invited person will have a seat in the graduation ceremony?
Transcribed Image Text:1. (a) (b) 2. Peter usually goes to the river in his neighborhood to catch fishes over the weekends. Based on his experience in the past, he could catch 3 fishes per hour on average. Assume the number of caught fishes has a Poisson distribution. What is the probability that he catches at least 2 fishes in a given 30 minutes? Use exponential distribution to find the probability that no fishes are caught in a given 20 minutes. (a) (b) When a hand of 5 cards is dealt from a standard deck of 52 cards, what is the probability that a full-house is obtained? (ex: aaabb) When a hand of 5 cards is dealt to each of three players, what is the probability that no one receive Aces? (a) 3. Consider a special six sided die with one blue face, two green faces and three red faces. When the die is rolled 3 times, if it's known that no blue face is obtained, what is the probability that more red faces than green faces are obtained? (b) [ When the die is rolled 30 times, what is the probability of getting green faces between 11 and 13 times? 4. Let the pdf of a continuous random variable X be defined as f(x)= if-3 ≤ x < 0 if 0 ≤ x ≤ 1 otherwise (a) (b) ((x+3)/6 (1-x)/2 .0 Find the cdf of X. Find E(X) and Var(X). 5. In a supermarket, the weights of apples and pears have approximately normal distributions. The weight of apples has the mean 150 g and the standard deviation of 15 g; the weight of pears has the mean of 200 g and the standard deviation of 25 g. (a) When a pear and two apples are randomly chosen, what is the probability that their total weight exceeds 540 g? (b) Assume apples cost 0.6 cent per gram and pears cost 0.5 cents per gram. When an apple and a pear are randomly chosen, what is the probability that the apple costs more than the pear? In a college, 400 students are graduating this semester. According to the school policy, each student is allowed to invite up to 3 people to the graduation ceremony. Based on the experience from the past, the school estimates the probabilities that a student will bring 0, 1, 2, and 3 people are 10%, 40%, 30% and 20% respectively. Assume the estimation is correct and the college prepares 680 chairs for the invited people, what is the probability that every invited person will have a seat in the graduation ceremony?
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