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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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Arte-miy333 [17]

Answer:

A cup of juice will cost 1.04 US dollars

Step-by-step explanation:

Here, we want to know the cost of one cup of juice in US dollars.

The cost of a quart of juice is Canada is 4.40CAN

now, since there are 4 cups in a quart, the cost of a cup of juice will be 4.40/4 = 1.10 CAN

Moving on;

We are told that 1 USD = 1.06 CAN ;

thus x usd = 1.10 CAN

1 * 1.10 = x * 1.06

x = 1.10/1.06

x = 1.037 which is approximately 1.04 USD

5 0
3 years ago
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vichka [17]

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4 0
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Line A is perpendicular to line B. The slope of line A is -1/9 what is the slope of line b?
Pani-rosa [81]
\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}}
{\stackrel{slope}{-\cfrac{1}{9}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{9}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{9}{1}}\implies 9}
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Wouldn't it be -1 I keep getting me wrong answer
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6 0
3 years ago
Two congruent 30-60-90 triangles are placed,as shown,so that they overlap partly and their hypotenuses coincide. If the hypotenu
Ede4ka [16]

Answer: The area common to both triangle is 31.77 sq. cm.

Step-by-step explanation:

Since we have given that

30-60-90 triangles are placed.

So, the ratio of sides would be

1:\sqrt{3}:2

Since Hypotenuse = 12 cm

So, it becomes,

2x=12\\\\x=\dfrac{12}{2}=6

So, Base would be

x=6\ cm

and Perpendicular would be

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So, Area common to the both triangles would be

\dfrac{1}{2}\times base\times height\\\\=\dfrac{1}{2}\times 6\times 6\sqrt{3}\\\\=18\sqrt{3}\\\\=31.177

Hence, the area common to both triangle is 31.77 sq. cm.

4 0
3 years ago
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