The discussion centers on calculating the probabilities x and y for the random variable Z, given specific values and their probabilities. The values provided are z = 2, 3, 5 with probabilities of 1/6 each, while z = 7 and z = 11 have unknown probabilities x and y. The expected value E(Z) is given as 5 + 2/3. The key equations derived are 7x + 11y = 4 and the requirement that the total probabilities must equal 1, leading to the solution of x and y.
PREREQUISITESStudents in statistics or probability courses, educators teaching probability concepts, and anyone looking to enhance their understanding of random variables and expected values.
kylebutler said:Homework Statement
z = 2, P(Z=z)=1/6
z = 3, P(Z=z)=1/6
z = 5, P(Z=z)=1/6
z = 7, P(Z=z)= x
z = 11, P(Z=z)= y
I'm supposed to find x and y given that E(Z)= 5+2/3
I have no idea how to do this. All I got is 7x+11x=4 but I can't solve this
LCKurtz said:I think you mean you got 7x+11y = 4. To get another equation remember that the Z probabilities must add to 1.