If X has the probability distribution f(x) = for x = 1,2,3,4,5. 15 (a) Find the...
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If X has the probability distribution f(x) = for x = 1,2,3,4,5. 15 (a) Find the cumulative distribution of X. (b) Find P(1<X ≤4.5). (15 points) If X has the cumulative distribution F(x)= 0, for x < 1 1 6' 1 3' (a) Find P(2<X ≤7). (b) Find the probability distribution of X. for 1 < x < 4 1 2' 1, for x > 10. for 4 < x < 6 (a) Evaluate the constant C in the p.d.f.. (b) Derive the c.d.f. for T. for 6 < x < 10 (20 points) A continuous random variable T has p.d.f. defined as t f(t)=C. (1² + 1)² for t> 0 and f(t) = 0 elsewhere. If X has the probability distribution f(x) = for x = 1,2,3,4,5. 15 (a) Find the cumulative distribution of X. (b) Find P(1<X ≤4.5). (15 points) If X has the cumulative distribution F(x)= 0, for x < 1 1 6' 1 3' (a) Find P(2<X ≤7). (b) Find the probability distribution of X. for 1 < x < 4 1 2' 1, for x > 10. for 4 < x < 6 (a) Evaluate the constant C in the p.d.f.. (b) Derive the c.d.f. for T. for 6 < x < 10 (20 points) A continuous random variable T has p.d.f. defined as t f(t)=C. (1² + 1)² for t> 0 and f(t) = 0 elsewhere.
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