Stats Help Please?

Two questions


1. Two cards are drawn at random from a pack of cards with replacement. Let the random variable X be the number of cards drawn from the heart suit. a) construct the probability mass function. b)construct the cumulative distribution function. c) what is the most likely value of the random variable X?


2. An archer shoots an arrow at a circular target with a radius of 50 cm. If the arrow hits the target, the distance r between the point of impact and the center of the target is measured. Suppose that this distance has a cumulative distribution function F(r)=A+(B/(r+5))^3) for 0%26lt;r%26gt;50. a)find the values of A and B. b) what is the probability that the arrow hits within 10 cm of the center of the target? c)what is the probability that the arrow hits more than 30 cm away form the center of the target?





Any help would be appreciated, I'm doing independent study. If you know the answer would you please show how you did it too.

Stats Help Please?
1. a) and b) the numbers will be given in terms of X, pmf and cdf.





X = 0 pmf = 9/16 cdf = 9/16


X = 1 pmf = 6/16 cdf = 15/16


X = 2 pmf = 1/16 cdf = 16/16





there are 13 hearts in the deck (and thirteen cards of every suit) since there are 4 suits you have a (1/4) likelihood of drawing a heart on any given draw since there is replacement (and therefore a likelihood of 3/4 of not drawing a heart).





P(X = 0) = P(no heart) * P(no heart) assuming draws are independent = 3/4 * 3/4 = 9/16


P(X = 2) = P(heart) * P(heart) = 1/4 * 1/4 = 1/16


Since the only other option is P(X = 1) and P(X = 0) + P(X = 1) + P(X = 2) = 1, P(X = 1) = 6/16 = 1 - 9/16 - 1/16





c. Most likely value of X = E(X) = sum x * f(x) where f(x) is the pmf of x.


E(X) = 0*9/16 + 1*6/16 + 2*1/16 = 8/16 = 1/2


at least this is my interpretation, the most likely value to be drawn is 0, but I think they are asking for the expected value. You can decide how you feel about that one.





2. a) you know that the integral of f(r) over all r is equal to 1. Since you are given F(r), F(50) - F(0) has to equal one. However, I can find no distinct value of A. Maybe there's a missing ( at the beginning of the F(r) equation?





b. that is like the integral from 0 to 10 of f(r) = F(10) - F(0) which can be done since you've solved for A and B.





c. integral 30 to infinity, but since the upper limit is 50 it's the integral 30 to 50 = F(50) - F(30)





Good luck.
Reply:u pay a friend to do it
Reply:LOL that is why i dropped out of AP Stat last week