7.1 Let X be a random variable with probabilitySi. 1= 1,2, 3,S(2) =10 elsewhere.Find the probability distribution of the random vari-able Y = 2X 1.7.8 A dealer's profit, in units of $5000, on a new au-tomobile is given by Y = X², where Xvariable having the density functionsa randomS(z) =2(1 - 2), 0

Answered: Image /qna-images/answer/d7c1e8f1-2545-4f98-9dcf-7ea73b7ae37a.jpg

Answered: 1 Let X be a random variable with…

1 Let X be a random variable with probability S(z) = { z=1,2,3. 1= 1,2,3, l0, elsewhere. nd the probability distribution of the random vari- le Y = 2X - 1.

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Question

7.1 Let X be a random variable with probability
Si. 1= 1,2, 3,
S(2) =10 elsewhere.
Find the probability distribution of the random vari-
able Y = 2X 1.
7.8 A dealer's profit, in units of $5000, on a new au-
tomobile is given by Y = X², where X
variable having the density function
sa random
S(z) =2(1 - 2), 0<r<1,
10,
elsewhere.
(a) Find the probability density function of the random
variable Y.
(b) Using the density function ofY, find the probabil-
ity that the profit on the next new automobile sold
by this dealership will be less than $500.

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