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Ludmilka [50]
3 years ago
13

For each of the following sequences, determine whether it converges in probability to a constant. If it does, enter the value of

the limit. If it does not, enter the number "999".
1) Let X1,X2,… be independent continuous random variables, each uniformly distributed between −1 and 1.
a) Let Ui=X1+X2+⋯+Xii, i=1,2,…. What value does the sequence Ui converge to in probability? (If it does not converge, enter the number "999". Similarly in all below.)
b) Let Σi=X1+X2+⋯+Xi, i=1,2,…. What value does the sequence Σi converge to in probability?
c) Let Ii=1 if Xi≥1/2, and Ii=0, otherwise. Define,
Si=I1+I2+⋯+Iii.
What value does the sequence Si converge to, in probability?
d) Let Wi=max{X1,…,Xi}, i=1,2,…. What value does the sequence Wi converge to in probability?
e) Let Vi=X1⋅X2⋯Xi, i=1,2,…. What value does the sequence Vi converge to in probability?
2) Let X1,X2,…, be independent identically distributed random variables with E[Xi]=2 and Var(Xi)=9, and let Yi=Xi/2i.
a) What value does the sequence Yi converge to in probability?
b) Let An=1n∑i=1nYi. What value does the sequence An converge to in probability?
c) Let Zi=13Xi+23Xi+1 for i=1,2,…, and let Mn=1n∑i=1nZi for n=1,2,…. What value does the sequence Mn converge to in probability?

Mathematics
1 answer:
nikklg [1K]3 years ago
6 0

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below for the step by step explanation to the question above.

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stich3 [128]

Mario says that the expression 4+3n^2 has four terms: 4, 3, n, and 2. Mario is incorrect

<em><u>Solution:</u></em>

Given that the expression is:

4+3n^2

Given that, Mario says that the above expression has four terms

But Mraio is incorrect

Because the given expression has two terms only

4 is one of the term

3n^2 is another term

So there are totally 2 terms only

A term can be a signed number, a variable, or a constant multiplied by a variable or variables

Here 3 is a constant multiplied by n^2

So, 3n^2 is one term

Each term in an algebraic expression is separated by a + sign or - sign

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8 0
2 years ago
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podryga [215]
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so Pythagorean theorem says
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so
(2x+1)^2+(11x+5)^2=(12x+1)^2
distribute
(4x^2+4x+1)+(121x^2+110x+25)=(144x^2+24x+1)
add like terms
125x^2+114x+26=144x^2+24x+1
subtract 125x^2 from both sides
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subtract 114x from both sides
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subtract 26 from both sides
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factor
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therefor x-5=0 and/or 19x+5=0
so
x-5=0 add 5 to both sides
x=5
19x+5=0
subtract 5 from both sides
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since side legnths can't be negative, we can cross this solution out

so x=5
subtitute
1+2x
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1+10=11
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11x+5
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add them all up
side a+b+c=11+60+61=132=total legnth
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marshall27 [118]
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Answer:

first one: a,d,e

second one: d

Step-by-step explanation:

pemdas

6 0
3 years ago
Read 2 more answers
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