Show all work and plnce all answers in the spaces previded. Penoil only please 1

Question

Show all work and plnce all answers in the spaces previded. Penoil only please 1. Rx)- (+4)/ao. x-0, 1, 2, 3 in a probability ans funetion (pmt (a) Find 1B00 (b) Find the Var X)? 2. Let E00 =-5; and ECX-3y-89. what is etandartderiation of X? Let the random variable X be the number of traffic accidents per hour in a city between 4:00 pm and 7:00 pm. Assume X has a Poisson distribution with a mean of 6 accidents per hour. 3. (a) What is the probability there will be no accidenta in a given hour? (b) What is P(X 6)? (c) What is the P(5sX

Explanation / Answer

Question 1:

Here from the given probabiltiy density function, we get the PDF for X here as:

P(X = 0) = (0 + 4)/30 = (2/15)
P(X = 1) = (1 + 4)/30 = (1/6)
P(X = 2) = (4 + 4)/30 = (4/15)
P(X = 3) = (9 + 4)/30 = (13/30)

a) The expected value of X here is computed as:

E(X) = 0*(2/15) + 1*(1/6) + 2*(4/15) + 3*(13/30) = 2

Therefore E(X) = 2

b) The second moment of X here is computed as:

E(X2) = 0*(2/15) + 12*(1/6) + 22*(4/15) + 32*(13/30) = 5.1333

Therefore, we get here:

Var(X) = E(X2) - [ E(X)]2 = 5.1333 - 22 = 1.1333

Therefore Var(X) = 1.1333

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---