Probability-Definitions and Axiomatic Approach (ISS Statistics Paper I (Old Subjective Pattern)): Questions 1 - 2 of 2

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Question number: 1

» Probability » Definitions and Axiomatic Approach

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Let X be a random variable defined on (Ω, A, P). Define a point function F (x) =P {ω: X (ω) ≤ x}, for all xϵR. Shoe that the function F is indeed a distribution function.

Explanation

Let x 1 < x 2. Then (-∞, x 1] ( (-∞, x 2] and we have

F(x1)=P(Xx1)P(Xx2)=F(x2)

Since F… (264 more words) …

Question number: 2

» Probability » Definitions and Axiomatic Approach

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Let X have the density function,

f(x)={c(1x2), X <10,otherwise

(i) Find the constant c.

(ii) Find the distribution function.

(iii) Compute P [X > -1/2].

Explanation

(I) To find the value of c using this density function, the integral of density is equal to one by probability definition. The range of X is|X| < 1

X={1Xispositive1Xisn… (224 more words) …

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