6 Find critical value t002513 and t09955 for student tdistri

6. Find critical value t0:025;13 and t0:995;5 for student t-distribution.
7. Given a random sample of size n = 25 from standard normal population,
nd value k such that P(??2:069 < T < k) = 0:965, where T is the sum of all
samples.
8.Consider
ipping one fair six-sided die, so that S = f1; 2; 3; 4; 5; 6g, and
P(s) = 1
6 for all s 2 S. Let X be the number showing on the die, so that
X(s) = s for s 2 S, Let Y = X2. Compute the cumulative distribution func-
tion FY (y) = P(Y y), for all possible values of y.
9. Let X Exponential(), Let Y = X3, compute the density fy of Y.
10. Given an example of a random variable X such that E(min(X; 100)) =
E(X)=2

Solution

one tailed t_{0.025, 13} = 2.1604

t_0.995,5 one tailed = 2.5706

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7) P(-2.069<T<k) =0.965 T is the sum of samples of size 25

Hence Mean x bar = T/25

P(-0.08<z<0.04k) = 0.965 =0.0319+0.0.9331

From z table we find that 0.04k = 1.50since 09331 = (0.4331+0.5) and z corresponding to 0.4331 is 1.5

k = 37.50

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8) Y = x²

Y takes values as 1,4,9,16,25,36

p = 1/6 each,.

Cumulative prob function for y = x² is given below