Let X be a random variable with the probability density function given by 1 f(x)=xe-kx, 0 0. (i) (ii)…

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Let X be a random variable with the probability density function given by 1 f(x)=xe-kx, 0 0. (i) (ii)…

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Let X be a random variable with the probability density function given by

1

f(x)=√x²e-kx,

0

(i)

(ii)

(iii)

Tunjukkan bahawa k =dan seterusnya, camkan taburan bagi

X.

Show that k =and hence, identify the distribution of X.

Tentukan persentil ke-90 bagi X.

Determine the 90th percentile of X

Cari varians bagi X.

Find the variance of X.

0.90 = P(xx)

(7 markah/marks)

3/6

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