Let p(y) denote the probability function associated with a
Poisson random variable with mean λ. Show...
Let p(y) denote the probability function associated with a
Poisson random variable with mean λ. Show that the ratio of
successive probabilities satisfies (p(y)/p(y-1)) = ( λ /y), for
y=1,2,...
Let Y denote a random variable that has a Poisson
distribution with mean λ = 6. (Round your answers to three
decimal places.)
(a) Find P(Y = 9).
(b) Find P(Y ≥ 9).
(c) Find P(Y < 9).
(d) Find P(Y ≥
9|Y ≥ 6).
Let XiXi for i=1,2,3,…i=1,2,3,… be a random variable whose
probability distribution is Poisson with parameter λ=9λ=9. Assume
the Xi are independent. Note that Poisson distributions are
discrete.
Let Sn=X1+⋯+Xn.
To use a Normal distribution to approximate P(550≤S64≤600), we use
the area from a lower bound of __ to an upper bound of __ under a
Normal curve with center (average) at __ and spread (standard
deviation) of __ .
The estimated probability is __
Let Y be a discrete random variable with probability mass
function given by P(Y =i)=c·(i−2) fori=3,4,6
1. Pay attention to the possible values for Y , and find the
numerical value of c. Make sure to show work / justify your
answer.
2. Draw the graph of the cumulative distribution function of
Y.
The probability function of a random variable Y is given as
follows. ?(? = ?) = { 0.20, ? = 48 // 0.45, ? = 15 /// 0.14, ? = 32
// 0.05, ? = 43 /// 0.16, ? = 54 /// 0, ?. ?.
a) Find the range of the random variable Y.
b) Find the expected value and standard deviation of Y.
c) Let ? = ? 10 + 2.70,
Find the expected value and variance of X
(a) Let X be a binomial random variable with parameters (n, p).
Let Y be a binomial random variable with parameters (m, p).
What is the pdf of the random variable Z=X+Y?
(b) Let X and Y be indpenednet random variables. Let Z=X+Y.
What is the moment generating function for Z in terms of those
for X and Y?
Confirm your answer to the previous problem (a) via moment
generating functions.
Question 3 options:
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Let Z denote a standard normal random variable. Find the
probability P(Z < 0.81)? The area to the LEFT of 0.81?
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Enter in format X.XX rounding UP so one-half
(1/2) is 0.50 and two-thirds (2/3) is 0.67 with rounding. Enter
-1.376 as -1.38 with rounding. NOTE: DO NOT ENTER
A PERCENTAGE (%).
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Let Z denote a standard normal random variable. Find the
probability P(Z > -1.29)? The area to the RIGHT of...
Let T∈ L(V), and let p ∈ P(F) be a polynomial. Show that if p(λ)
is an eigenvalue of p(T), then λ is an eigenvalue of T. Under the
additional assumption that V is a complex vector space, and
conclude that {μ | λ an eigenvalue of p(T)} = {p(λ) | λan
eigenvalue of T}.
Let Xi be a random variable that takes on the value 1 with
probability p and the value 0 with probability q = 1 − p. As we
have learnt, this type of random variable is referred to as a
Bernoulli trial. This is a special case of a Binomial random
variable with n = 1.
a. Show the expected value that E(Xi)=p, and Var(Xi)=pq
b. One of the most common laboratory tests performed on any
routine medical examination is...
An
honest coin is tossed n=3600 times. Let the random variable Y
denote the number of tails tossed. Use the 68-95-99.7 rule to
determine the chances of the outcomes. (A) Estimate the chances
that Y will fall somewhere between 1800 and 1860. (B) Estimate the
chances that Y will fall somewhere between 1860 and 1890.