Question
In: Statistics and Probability
(a) Please write down the p.m.f of the binomial distribution X∼B(30,.4) and compute P(X∈[15,17]). (b) Please...
(a) Please write down the p.m.f of the binomial distribution X∼B(30,.4) and compute P(X∈[15,17]).
(b) Please write down the p.d.f of Normal distribution N(μ,σ2) and compute the mean, median, mode of N(4,16).
Solutions
orchestra answered 1 year agoRelated Solutions
Suppose that X ~ NB(r, p) [negative binomial distribution] and that Y ~ B(n, p) [binomial]....
Suppose that X ~ NB(r, p) [negative binomial distribution] and
that Y ~ B(n, p) [binomial].
a. Give a probabilistic argument to show that P(X > n) = P(Y
< r).
b. Use the FPF to express the equality in part (a) in terms of
PMFs.
c. Using the complementation rule, how many terms of the PMF of
X must be evaluated to determine P(X > n)?
d. How many terms of the PMF of Y must be evaluated to...
If X has a binomial distribution with p = 0.5, then the distribution of X is...
If X has a binomial distribution with p = 0.5, then the
distribution of X is _______.
a)left-skewed
b)uniform
c)right-skewed
d)symmetric
Binomial Distribution. Suppose that X has a binomial distribution with n = 50 and p =...
Binomial Distribution. Suppose that X has a binomial
distribution with n = 50 and p = 0.6. Use Minitab to simulate 40
values of X.
MTB > random 40 c1;
SUBC > binomial 50 0.6.
Note: To find P(X < k) for any k > 0, use ‘cdf’ command;
this works by typing:
MTB > cdf;
SUBC > binomial 50 0.6.
(a) What proportion of your values are less than 30? (b) What is
the exact probability that X will...
For each problem, write an R code to compute each probability. (a) Binomial Distribution: X ~...
For each problem, write an R code to compute each
probability.
(a) Binomial Distribution: X ~ Bin(10, 0.7)
(i)
P(X
= 2)
(ii)
P(X
< 2)
(iii)
P(X >
2)
(iv)
P(1 < X
< 7)
(b) Normal Distribution: X ~ N(0, 4). Note that variance is 4
and, hence, the standard deviation is 2.
(i)
P(X
< 3)
(ii)
P(X
> 3)
(iii)
P(1 < X
< 3)
(c) Choose either (a) or (b) and interpret the results in...
If X follows a binomial(5, 0.15), determine (a) P(X = 0). (b) P(X ≤ 4). (c)...
If X follows a binomial(5, 0.15), determine
(a) P(X = 0).
(b) P(X ≤ 4).
(c) P(X > 1).
Consider a binomial experiment with n=13 and p=0.3 a. Compute f(0) (to 4 decimals). b. Compute...
Consider a binomial
experiment with n=13 and p=0.3
a.
Compute f(0) (to 4 decimals).
b.
Compute f(8) (to 4 decimals).
c.
Compute P(x<=2) (to 4 decimals).
d.
Compute P(x>=4) (to 4 decimals).
e.
Compute E(x) (to 1 decimal).
f.
Compute Var(x) and ó.
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used...
Compute P(X) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(X) using the normal
distribution and compare the result with the exact probability.
nequals62, pequals0.3, and Xequals8
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used...
Compute P(X) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(X) using the normal
distribution and compare the result with the exact probability.
n=40, p=0.35, X=20 P (X) = Can the normal distribution be used to
approximate thisprobability? Approximate P(X) using the normal
distribution. Use a standard normal distribution table. Select the
correct choice below and fill in any answer boxes in your choice.
By how much...
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used...
Compute P(X) using the binomial probability formula.
Then determine whether the normal distribution can be used to
estimate this probability. If so, approximate P(X) using the
normal distribution and compare the result with the exact
probability.
n=40, p=0.35, X=20
P (X) =
Can the normal distribution be used to approximate this
probability?
Approximate P(X) using the normal distribution. Use a standard
normal distribution table. Select the correct choice below and fill
in any answer boxes in your choice.
By how...
Find the following probabilities. A.) P(X=5), X FOLLOWING A BINOMIAL DISTRIBUTION, WITH N=50 AND P=.7. B.)...
Find the following probabilities.
A.) P(X=5), X FOLLOWING A BINOMIAL DISTRIBUTION, WITH N=50 AND
P=.7.
B.) P(X = 5), X following a Uniform distribution on the interval
[3,7].
c.) P(X = 5), X following a Normal distribution, with µ = 3, and
σ = .7.
(To complete successfully this homework on Stochastic Models,
you need to use one of the software tools: Excel, SPSS or
Mathematica, to answer the following items, and print out your
results directly from the software....
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