I know this could be solve using the gamma function, is there other way to solve this problem? if so could someone show me how to do it both ways, meaning using the gamma function and any other way possible. please be as detailed as possible. Thank you and I'll rate
Homework Answers
Y is sample mean
since n = 40 > 30
we can approximate it using normal distribution
E(Y) = 1/lambda = 1/ 0.4 = 2.5
sd(Y) = 2.5/sqrt(40) = 0.39528
P(Y < 2)
= P(Z <(2 - 2.5)/0.39528)
= P (Z<−1.26)=0.1038
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I know this could be solve using the gamma function,
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For random variable X, X Bi( 300, . 1) find probabilities : P( X > 35), P( 28 CX < 31) Let Yi, Y2,..., Yso be a sequence of exponentially distributed random variable with parameter λ=.4, and Y=Σ Y/40. Find P(Y<2) 40 7 projector-1&messa google.com/mail/u/0/#inbox/FMfcgxwBVCzcfjWVpqNzGmrwWBgGqrN? gePartid=0.2
which way is the simplest way of solving this problem? is there other ways to solve...
which way is the simplest way of solving this problem?
is there other ways to solve it without using gamma function? if
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lambda=.4 please show all steps!! as detailed as possible, thank you so much for your time...
lambda=.4 please show all steps!! as detailed as
possible, thank you so much for your time
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which way is the simplest to solve this problem? is
there other way than using gamma function ? please add the
different ways to solve this problem. Thank you !!!
For random variable X, X Bi( 300, . 1) find probabilities : P( X > 35), P( 28 CX < 31) Let Yi, Y2,..., Yso be a sequence of exponentially distributed random variable with parameter λ=.4, and Y=Σ Y/40. Find P(Y<2) 40 7 projector-1&messa google.com/mail/u/0/#inbox/FMfcgxwBVCzcfjWVpqNzGmrwWBgGqrN? gePartid=0.2
which way is the simplest way of solving this problem?
is there other ways to solve it without using gamma function? if
so, please show the different ways! thank you so much !
Let Yi, Y2, ..., Yso be a sequence of exponentially distributed random variable with parameter-4 , and Y =/i/40. Find P(Y<2) 40 /mail.google.com/mail/u/0/#inbox/FMcgxwBVCzcfwVpqNzGmrwWBgGqrN?projector-1 &messagePartid=0.2
lambda=.4 please show all steps!! as detailed as
possible, thank you so much for your time
Let Yi, Y2, ..., Yso be a sequence of exponentially distributed random variable with parameter λ=.4 , and Y-31/40, Find P(Y<2) 40
The moment generating function (MGF) for a random variable X is: Mx (t) = E[e'X]. Onc useful property of moment generating functions is that they make it relatively casy to compute weighted sums of independent random variables: Z=aX+BY M26) - Mx(at)My (Bt). (A) Derive the MGF for a Poisson random variable X with parameter 1. (B) Let X be a Poisson random variable with parameter 1, as above, and let y be a Poisson random variable with parameter y. X...
Suppose we have 5 independent and identically distributed random variables Xi,X2.X3,X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y -XX. The density function of Y is (a) Poisson with λ-40 (b) Gamma with α-10 and λ-8 (c) Normal with μ-40 and σ-3.162 (d) Exponential with λ = 50 (e) Normal with μ-50 and σ2-15
(1 point) In Unit 3, I claimed that the sum of independent, identically distributed exponential random variables is a gamma random variable. Now that we know about moment generating functions, we can prove it. Let X be exponential with mean A 4. The density is 4 a) Find the moment generating function of X, and evaluate at t 3.9 The mgf of a gamma is more tedious to find, so l'll give it to you here. Let W Gamma(n, A...
Consider the simplified Bayesian model for normal data The joint posterior pdf is ful, σ21 x)a(σ2,-/2-1 expl_jy.tx, _aPI The marginal posterior pdfs of μ and σ 2 can be obtained by integrating out the other variable (8.30) y@1 x) α (σ2)-m;,-1/2 expl-- Σ.-tri-x)2 (8.31) d. Let q1 and q2 be they/2 and 1-y/2 quantiles of (8.31). Show that the 1-γ credible interval (gi,q2) is identical to the classic confidence interval (5.19) (with ar replaced by y). Hence, a (1-α) stochastic...
Let X1,X2 be two independent
exponential random variables with λ=1, compute the
P(X1+X2<t) using the joint density function. And let Z be gamma
random variable with parameters (2,1). Compute the probability that
P(Z < t). And what you can find by comparing P(X1+X2<t) and
P(Z < t)? And compare P(X1+X2+X3<t) Xi iid
(independent and identically distributed) ~Exp(1) and P(Z < t)
Z~Gamma(3,1) (You don’t have to compute)
(Hint: You can use the fact that Γ(2)=1,
Γ(3)=2)
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