Linear Combinations of Random Variables
189 questions· page 1 of 19
The random variables and have the independent distributions and respectively.
Find .
Each day, people independently use the video game.
Find the mean and variance of the total amount paid by people.
In Urberia, the masses, in kilograms, of men have the distribution . A certain footbridge in Urberia can take a maximum safe load of 1500 kg. When men stand on the bridge, the probability that the bridge is unsafe is less than 0.01.
Stating a necessary assumption, find the maximum value of .
Candidates for a certain diploma take two tests. Their marks for the first test and the second test are modelled by the independent variables with distributions and respectively. The final mark, , for each candidate is found by doubling the mark in the first test and adding the result to the mark in the second test.
Find the probability that the mean, , of the final marks of a random sample of 25 candidates is greater than 143.
Find the probability that the total mass of a randomly chosen large bag of potatoes and a randomly chosen small bag of potatoes is more than 3.55 kg.
Find the probability that the mass of a randomly chosen large bag of potatoes is less than 3 times the mass of a randomly chosen small bag of potatoes.
Find the probability that the total mass of a randomly chosen large bag of potatoes and a randomly chosen small bag of potatoes is more than 3.55kg.
Find the probability that the mass of a randomly chosen large bag of potatoes is less than 3 times the mass of a randomly chosen small bag of potatoes.
The price of tomatoes is $4.30 per kg.
A large bag of tomatoes and a small bag of tomatoes are chosen at random. Find the probability that the total price of the tomatoes in the two bags is less than $16.
Find the probability that in a randomly chosen year the firm uses more gasoline than diesel fuel.
The costs per litre of gasoline and diesel fuel are $0.80 and $0.85 respectively.
Find the probability that the total cost of gasoline and diesel fuel in a randomly chosen year is between $20,000 and $22,000.