emilyhh
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I am stuck on this further maths question

1.​​The discrete random variable X has probability distribution given by
​​
x
2
3
6
11
P(X = x)

a

b
​​The discrete random variable .
​​Given that E(Y) = 50.3
​​(a) find the value of a and the value of b.
​(3)
​​(b) Find P(9 – Y > 0).
​(2)

​​Independent observations of X are taken.
​​The random variable T represents the total number of these 120 observations that are even.
​​(c) Find
​​​(i) E(T ),

​​​(ii) Var(T ).
​(2)
​​(d) Find, using a suitable approximation, P(T > 10).
​(3)
(Total for Question 1 is 10 marks)

i’ve done part a and b but for c i’m not sure if the expectation and var need to be timesed by 120 or not
can anyone help?
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davros
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(Original post by emilyhh)
I am stuck on this further maths question

1.The discrete random variable X has probability distribution given by

x
2
3
6
11
P(X = x)

a

b
The discrete random variable .
Given that E(Y) = 50.3
(a) find the value of a and the value of b.
(3)
(b) Find P(9 – Y > 0).
(2)

Independent observations of X are taken.
The random variable T represents the total number of these 120 observations that are even.
(c) Find
(i) E(T ),

(ii) Var(T ).
(2)
(d) Find, using a suitable approximation, P(T > 10).
(3)
(Total for Question 1 is 10 marks)

i’ve done part a and b but for c i’m not sure if the expectation and var need to be timesed by 120 or not
can anyone help?
Could you possibly upload an image of the complete question? It looks like some details are missing from your transcription of the information
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emilyhh
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(Original post by davros)
Could you possibly upload an image of the complete question? It looks like some details are missing from your transcription of the information
Name:  BE5F3120-AD53-4109-8995-26E030C31857.jpeg
Views: 8
Size:  110.4 KByes of course is that better?
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DFranklin
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You ask: i’m not sure if the expectation and var need to be timesed by 120

This implies you have an expectation/variance for a random variable that you think you should multiply by 120.

What, *exactly*, is that random variable,?
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emilyhh
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(Original post by DFranklin)
You ask: i’m not sure if the expectation and var need to be timesed by 120

This implies you have an expectation/variance for a random variable that you think you should multiply by 120.

What, *exactly*, is that random variable,?
I tried to find the expectation of T which I did by timesing 2 by 1/50 and 6 by 1/25 and adding them to get 7/25 which I thought would be the expectation of the even numbers as the 3 and 11 are both odd I thought I might need to times the 7/25 by 120 which gives 33.6 as there are 120 observations I might be doing it completely wrong though
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DFranklin
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The question asks for the expectation of the *number* of even observations.

The standard way of answering a question like this is to define a r.v. E such that E = 1 if X is even, 0 otherwise.

Then the number of even observations in 120 trials is the sum of 120 i.i.d. random variables with distribution E. (So you find exp/var of E and use linearity of exp / var to find the sum of 120 copies of E).
Last edited by DFranklin; 3 weeks ago
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