Download Midterm Exam with Solutions | Statistics for Engineers | STAT 4705 and more Exams Statistics in PDF only on Docsity! Midterm Exam Statistics 4705 10/3/97
Each problem is given equal weight. Show work for partial credit. Z. Ys O
> ‘The Stardust casino in Las Vegas plays blackjack using two decks shuffled together. This means
Va that the combined decks contain 104 cards that include 8 aces and 32 ten-valued cards. The
{_7 dealer is dealt one card face up and then one card face down without replacement. Compute the
Te) that the dealer has a ten-valued card down given that he has an ace up.
How many distinguishable orderings are there of the distinct letters in the word Hokie? How
many distinguishable orderings are there of the not-all-distinct lettera in the word statistics?
a) [20 3) 58,400
If 3 whales compare their birthoceans,
(a) What is the probability that all 3 of them were born different oceans? 3
(8) What is the probability that at least 2 of them are born in the same Géeat
{Assume that the probability is 1/7 of being born in each of the seven oceans.) {- Z
4. Consider the random variables X and Y with density function given by
x+y, O<x<l, O<y<l
wo ={
0 , elsewhere
bo, Give the marginal distribution of X. gO) * ye oa
{b) Find P(X > 0.5, Y > 0.5). he f a
5. Stppose that X and Y have the following joint probability distribution
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x
f(x, y) 2 4
a ; 1 | 0.20 0.05
y 2} 010 0.40
3 | 0.08 0.20
7}
x ee
Find th 1 distribut fx, 7 35 GF L 44
ind t! i istributi 4: «A =
(a) Find the marginal distribution of X, i) Dee “25
(b) Find the marginal distribution of Y,
(c) Find whether or not X and Y are independent random variables. Justify your answer.
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