4. The probability density function of a random variable Y is given by | 24y(10+2y-0.3y²) 0eve10 10000 0, otherwise Suppose a random sample of 40 observations is obtained from this distribution and these are denoted as Y,. Y,,.Y.

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4. The probability density function of a random variable Y is given by
24y(10+2y-0.3y)
f,(y)= {
2,0<y<10
10000
0,
otherwise
Suppose a random sample of 40 observations is obtained from this distribution and these
are denoted as Y,Y,,.Yg.
a) Approximate the probability that the sample sum T = Ey, is between 200 and 250.
b) Approximate the probability that the sample mean Y is less than 5.5.
Transcribed Image Text:4. The probability density function of a random variable Y is given by 24y(10+2y-0.3y) f,(y)= { 2,0<y<10 10000 0, otherwise Suppose a random sample of 40 observations is obtained from this distribution and these are denoted as Y,Y,,.Yg. a) Approximate the probability that the sample sum T = Ey, is between 200 and 250. b) Approximate the probability that the sample mean Y is less than 5.5.
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