5b let random variable x represent the number of heads minus the number of tails when a fair coin is tossed 9 times.
what is pr(x=0)?
what is pr(x=3)?
let random variable y represent the number of heads minus the number of tails when a fair coin is tossed 8 times.
what is pr(y=0)?
what is pr(y=3)?

Let be the number of times a coin lands heads up. Then the coin lands tails up times, and . follows a binomial distribution with and , so that

Then we have

because can only take on integer values. The other probability is

In terms of , we have and follows a binomial distribution with and the same probability as before, so that

Then we find

and

the correct answer is $7.38

step-by-step explanation:

asnwer is (g o h o f)(x) = 2x - 6/x + 7

step-by-step explanation:

given,

f(x) = x - 3/x

g(x) = x + 3

h(x) = 2x + 1

we need to find : (g o h o f)(x)

we can write (g o h o f)(x) = g[ h{ f(x) } ]

so first we find h{f(x)}

h{f(x)} = f(x) + 3 = (x - 3/x) + 3

h{f(x)} = x - 3/x + 3

now we find g[ h{ f(x) } ].

g[ h{ f(x) } ] = g(x - 3/x + 3)       {plug h{f(x)} = x - 3/x + 3 in g[h{f(x)}] }

g(x - 3/x + 3) = 2 (x - 3/x + 3) + 1

                    = 2x - 6/x + 6 + 1

                    = 2x - 6/x + 7

hence we get (g o h o f)(x) = 2x - 6/x + 7