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

2.1604 and 4.0322 (one tailed is given)

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k = 2.12

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