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Problem 1. Let Y be the density function given by f(y) = 1/5, −1 < y...

Problem 1. Let Y be the density function given by

f(y) = 1/5, −1 < y ≤ 0,

1/5 + cy, 0 < y ≤ 1

0, elsewhere.

1. Find the value of c that makes f(y) a density function.

2. Compute the probability P (−1/2 ≤ Y < 1/2)

3. Find the expected value µ and the standard deviation σ of

math   Statistics-And-Probability   
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Answer #1

The given density function of y is f(y) = -leyco = + cy os y el = 0 ow fcy) is pdf when & flyg dy=1. : dy + sf*cy dy are s (hp chap & the Ching 5 = th + OU (41** *097675 - 5 [++]+$13-6)*812-63 20 400 E (Y) = M = g g flysdy = jy. fladdy = syz de + SD/41++ (1407 * () Now, 02 E (42) = sy2 fcy) dy - Jy2.fcysty = $92.104+S42(+4)dy [*] + [9]+ FRED Et poft - [**+ ite, day = 2 +varcy)=02 130 EC42) - [[cy]² O -(0) 130 - 36 300 - 225 300 - Tvar(r) = 0. 27 ) : o=Vvarty) = 10.27

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