Link: http://i42.tinypic.com/34jf7ex.png
I seriously don't know where to start on number 7. And can you confirm that 6a) is correct. Thank you so much!
Link: http://i42.tinypic.com/34jf7ex.png
I seriously don't know where to start on number 7. And can you confirm that 6a) is correct. Thank you so much!
2. Show that for a binomial distribution B with a fixed number of trials n and a fixed probability p = 0.5, B(k) = B(n - k).
6. Suppose you flip a quarter 16 times and count the times it lands heads up.
a) What is the expected number of heads? 8?
b) What is the probability that the number of heads will be no more than one standard deviation from from the expected number?
7.Suppose the following experiment is conducted: A die with s sides marked 1 through s is tossed n times and the number of times a 1 is tossed is recorded. After many repetitions of the experiment, it is found that the number of 1s tossed has a mean of 33 and a standard deviation of 5.5.
a) If the die is assumed to be fair, what is the most likely number of sides it has?
b) If the die is assumed to be fair, how many times n was tossed in each experiment?
Q2. You should know that $\displaystyle B(x) = {n \choose x} p^x (1 - p)^{n - x} = {n \choose x} (0.5)^x (0.5)^{n - x}$. Substitute $\displaystyle x = k$ and $\displaystyle x = n - k$. What do you get?
Q6. X ~ Binomial(n = 16, p = 0.5).
(b) $\displaystyle \sigma = \sqrt{(16)(0.5)(0.5)} = 2$. So calculate $\displaystyle \Pr(6 \leq X \leq 10)$.
Let X be the random variable number of times a 1 is tossed.
X ~ Binomial(n, p = 1/s).
$\displaystyle \mu = np \Rightarrow 33 = \frac{n}{s}$ .... (1)
$\displaystyle \sigma^2 = n p (1 - p) \Rightarrow 5.5^2 = \frac{n (s - 1)}{s^2}$ .... (2)
Substitute (1) into (2) and solve for $\displaystyle s$. Hence solve for $\displaystyle n$.