Question

A biased coin has a 40% chance of producing a head. If it is tossed 10 times, What is the probability of getting exactly 3 heads? b. a. What is the probability of getting 3 or more heads. (This can be calculated in two different ways. The easier way uses the complement rule.) a. Find the value of C for which the function f(x) probability density function. b. Use your density function in (a) to find PCO s X 1) and P(l sX s5) c. Use your probability density function in (a) to compute the cumulative is a 0, otherwise distribution function F(x).

Answer 1

A, f(n) = {c x^2, 0 lessthanorequalto x lessthanorequalto 2 0, 0 w} integral^2_0 c x^2 dx = 1 or, c[x^3/3]^2_0 = 1 or, 8/3 c = 1 or, c = 3/8 b, a, p(0 lessthanorequalto x lessthanorequalto 1) = p(x lessthanorequalto 1) - p(x < 0) = p(x lessthanorequalto 1) = integral^1_0 3/8 x^2 dx = [3/8 x^3/3]^1_0 = 1/8 p(1 lessthanorequalto x lessthanorequalto 5) = p(x lessthanorequalto 5) - p(x < 1) = p(x lessthanorequalto 2) - p(x < 1) = 1 - 1/8 = 7/8 C. F(x) = integral^x_0 3/8 x^2 dx = 3/8 [x^3/3]^x_0 = x^3/8