# further maths

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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?

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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#2

(Original post by

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?

**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?

0

reply

(Original post by

Could you possibly upload an image of the complete question? It looks like some details are missing from your transcription of the information

**davros**)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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#4

You ask:

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’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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(Original post by

You ask:

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,?

**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,?

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#6

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).

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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