Suppose that (Ω, F, P) is Lebesgue measure on the interval [0, 1] Define random variables X(ω)=ω, Y(ω)=2ω+3 and Z(ω)=4ω+1 Compute P(X < b ∩ Y < c) and P(Z > a) as...

Suppose that (Ω, F, P) is Lebesgue measure on the interval [0, 1] Define random variables X(ω)=ω, Y(ω)=2ω+3 and Z(ω)=4ω+1 Compute P(X < b ∩ Y < c) and P(Z > a) as...

Draw 5 cards at random from the deck. For sums < 8 you win double that sum in dollars. For 8 ≤ sum ≤ 20 you lose half your sum in dollars. If sum > 20, you lose total sum in dollars. Find the...

With the Sample space being [0,1], suppose we are looking at a sequence of random variables Xn defined by Xωn = ωn . How can we prove that Xn converges to 0 in probability? And also what is its...

Four red cards and four green cards are well shuffled. Cards are drawn, without replacement, until the color of a card drawn matches the color of the first card drawn. Find the average number of cards...

Suppose that Z is a standard normal random variable. Compute Pr(Z<−1.54). (If needed, round answers to 3 decimal places)

a) P[Z< .62] b) P[Z < -.62] C) P[Z> 1.59] D) P[-1.3< Z< 2.61] E) P[|Z| < 1.65]

two marbles are drawn from a bag in which there are 4 red marbles and 2 blue marbles; the number of blue marbles is counted.

1) CBS and the NYT conducted a national poll of 1048 randomly selected 13 to 17-year olds and counted how many owned smart phones. The reporters were trying to decide whether more than half of teenagers...

how do I calculate the probability X1 > X2 where X1 and X2 are independent, normally distributed random variables?

I have an employee who has missed work twice in eleven years. I'm wondering if there is a way to show the probability of a random error like this occuring. Im not sure what information I may still...

Draw 5 cards at random from the deck. For sums < 8 you win double that sum in dollars. For 8 ≤ sum ≤ 20 you lose half your sum in dollars. If sum > 20, you lose total sum in dollars. Find the...

Draw 5 cards at random from the deck. For sums < 8 you win double that sum in dollars. For 8 ≤ sum ≤ 20 you lose half your sum in dollars. If sum > 20, you lose total sum in dollars. Find the...

mean and variance definition in random variable in probability

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