Question

Compute E(N^2), for N∼Geom(p), by conditioning on the outcome of the first trial. Use this to calculate Var(N)

Answer #1

The distribution of is

When a failure occurs on the first trial, (conditioning on the failure of first trial)

The conditional expectation is

Now the unconditional expectation is

Now the unconditional expectation is

The variance is

If X∼Binom(n,p), E[X] = np. Calculate V[X] = np(1−p) by:
a) First show E[X(X−1)] + E[X] − (E[X])^2 = V[X] (Hint: Use
propertie of E[·] and V[·]).
b) Show E[X(X−1)] = n(n−1)p^2
c) Use E[X] = np, a) and b) to discuss, V[X] = np(1−p).

consider a binomial experiment with n = 15 and p= 0.3.
a. compute f(0) (to 4 decimal places)
b. compute f(8) (to 4 decimal places)
c. compute P(x is less than or equal to 2) (to 4 decimal
places)
d. compute P( x is greater than or equal to 1) (to 4 decimal
places)
e. compute E(x) (to one decimal)
f. Compute Var(x) and sigma. (both to 2 decimal
places)

Question 5. Consider a binomial experiment with
n = 10 and p = 0.10. Use the binomial tables below to answer parts
(a) through (d).
Find f (0).
Find f (2).
Find P(x ≤ 2).
Find E(x).
Find Var(x) and σ

Assume that a procedure yields a binomial distribution with a
trial repeated n times. Use the binomial probability formula to
find the probability of x successes given the probability p of
success on a single trial.
n=5, x=2, p=0.55
P(2) = (Round to three decimal places as needed.)

1. It is given that L ~ Bin(n, p), where E(L) = 4 and Var(L) =
3.5.
(a) Find the values of n and p
(b) Find P(L =10)

1. Referring to the equation Var(P) = b2 Var(S) +
Var(e), the venture capitalist can calculate Var(e) to understand
the uncertainty that is attributable to the exchange rate
uncertainty.
True or FALSE?
2. Referring to the equation Var(P) = b2 Var(S) +
Var(e), the venture capitalist can calculate b2 Var(S)
to understand the part of the uncertainty that is independent of
exchange rate movements.
TRUE OR FALSE?
3. Referring to the equation Var(P) = b2 Var(S) +
Var(e), the venture...

Consider the following probability distribution table:
X
1
2
3
4
P(X)
.1
.2
.3
.4
If Y = 2+3X, E(Y) is:
A.7 B.8 C.11 D.2
19.
If Y=2+3X, Var (Y) is:
A.9
B.14
C.4
D.6
20.
Which of the following about the binomial distribution is not a
true statement?
A. The probability of success is constant from trial to trial.
B. Each outcome is independent of the other. C. Each outcome is
classified as either success or failure. D....

Assume that a procedure yields a binomial distribution with a
trial repeated n times. Use the binomial probability formula to
find the probability of x successes given the probability p of
success on a single trial. Round to three decimal places.
n = 7, x = 4 , p = 0.5

Assume that a procedure yields a binomial distribution with a
trial repeated n times. Use the binomial probability formula to
find the probability of x successes given the probability p of
success on a single trial. Round to three decimal places.
nequals5; xequals2; pequals0.70

In an experiment, there are n independent trials. For
each trial, there are three outcomes, A, B, and C. For each trial,
the probability of outcome A is 0.20; the probability of outcome B
is 0.30; and the probability of outcome C is 0.50. Suppose there
are 10 trials.
(a) Can we use the binomial experiment model to determine the
probability of four outcomes of type A, five of type B, and one of
type C? Explain.
No. A binomial...

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