Question: Toss a coin N times. For the probability of heads P(Heads) = x, with distribution fx(x) = 6x(1 x); 0 <1, determine: a. fN(n),

Toss a coin N times. For the probability of heads P(Heads) = x, with distribution fx(x) = 6x(1 – x); 0 <1, determine:

a. fN(n), f(x,n), f(n|x), and f(x|n),

b. P (N Heads),

c. E{n},

d. E {x|n),

e. p{x < ½ |n) leaving integral unevaluated.

Note that N is the number of trials and n the number of observed heads over this experiment.

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