STAT410- Homework #07 Solved

. After a homework assignment is posted on Compass2g, the weak-minded la7 lazy Chegg enthusiasts flock to Chegg according to a Poisson process wit the average rate of 1.5 weak-minded lazy Chegg enthusiasts per minute.

The pudding-brain lazy CourseHero worshipers show similar behavior. ) 



Find the probability that at most two weak-minded lazy Chegg enthusiastswould show up on Chegg during the first minute after the homewor assignment is posted on Compass2g 



Find the probability that exactly seven weak-minded lazy Chegg enthusiasts would show up on Chegg during the first five minutes after the 
homework assignment is posted on Compass2g. 



in STAT 410

d) 

7. 

weak-minded lazy Chegg enthusiast would show up on Chegg during the fifth minute after the homework assignment is posted on Compass2g. 

Construct a 90% prediction interval for the time when the seventh weak- minded lazy Chegg enthusiast would show up on Chegg. 

That is, find a and b such that 

Let ke GOT be a random sample from a probability distribution with probability density function Let and let x I ,X2, , Xn bearandom sample froma probability 

distribution with probability density function 

zero otherwise. 

in STAT 410 

_ (ii) 

Suppose n = 3, and _ 0.62, 1.54, x-s= 1.86. 

Find a method of moments estimate of V. 

Find E(X). It will depend on V, so it will bea function of V, say, h(v). 

Replace E(X) with i, so 

Solve for V. Adda tilde. 

(O Obtain a method of moments estimator of y, y. 

(O Obtain the maximum likelihood estimator of V , RIJ . (ii) Suppose n — 3, and 

x 1=0.62, x 2 1.54, x 3 1.86 

Find the maximum likelihood estimate of V. 

—That is, -find = argmax lnL(V), where L(v)— 

Multiply: L(v) * f(xl; V) •f(xn•, V). 

Simplify. "Hint": a • a = a 

Take ln. "Hint": Inb, 

Take the derivative with respect to V. 

Set equal to zero. Solve for V. Add a hat. 

_H—I-O 

follows a Gamma distribution. 

Show that W —In 1 

c) 

2 

What are the parameters and O for this Gamma distribution? creditwifå given 

Incl the maximum likelihood estimate of NJ 8. 

Let g > 0 and let x I ,X2, be a random sample from a probability 

distribution with probability density function 

zero elsewhere. 

2 

a). 

(i) 

Obtain the maximum likelihood estimator of 

Suppose n =5, —0.3, 0.6, 1.2, 1.3, .rs= 1.8. 

Obtain the maximum likelihood estimate of . 

That is, find In Where 1-(Z)— 

O Multiply: 

@ Simplify. — "Hint": —a b • ac = a 

b+C 

Take "Hint"; In 

@ Take the derivative with respect to 

- Set equal to zero. Solve for —j Add a hat. 

Show that W X 3 follows a Gamma distribution. 

b)