Find the constant k such that f(x) is probability density of a random variable X.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Assessment Scenario/Problem

Mathematical Statistics part

Note: for the other parts of coursework and deadline see the Coursework guidelines document on NOW.

Release dates:

31.March– Mathematical Statistics part

 Solve the following problems:

Probability distribution function is given by 

f(x)={(k/√x    for  0<x<n@0        elsewhere   )}

where  n value is equal to last three digits of your N number (for example students number N0123456 will give n=456.

Find the constant k such that f(x) is probability density of a random variable X.

Find E(X)  and σ^2.

Find E(X^3-3X^2+X+1).

Type your answers using Word or Latex, taking care of mathematical and overall presentation of your work. Try not to use more than 2 pages to answer this part of the coursework. For more detail see the marking grid attached.

 

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