The continuous random variable X has cdf given by xS-1 F (x) -) ar+a 2a x+a -1srs0 Osrs1 3a otherwise Determine the value of a; (i) the pdf of X. (b) In an examination, the marks obtained by students are normally distributed with mean u and standard deviation o. If 30% of the students have more than 70 marks and 12% of students have scored less than 55 marks, find the value u and o.

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(a),
The continuous random variable X has cdf given by
xS-1
-1srs0
F (x) - ar+a
2a x+a
Osrs1
3a
otherwise
Determine
) the value of a;
(i) the pdf of X.
(b) In an examination, the marks obtained by students are normally
distributed with mean u and standard deviation o. If 30% of the
students have more than 70 marks and 12% of students have scored less
than 55 marks, find the value u and o.
(c)
A die is tossed 60 times and the following frequencies are observed.
|outcome
Observed frequency
12 3 4| 5| 6
4 7
16
8.
8 7
Using a x test, test at 5% level whether the die is fair.
Transcribed Image Text:(a), The continuous random variable X has cdf given by xS-1 -1srs0 F (x) - ar+a 2a x+a Osrs1 3a otherwise Determine ) the value of a; (i) the pdf of X. (b) In an examination, the marks obtained by students are normally distributed with mean u and standard deviation o. If 30% of the students have more than 70 marks and 12% of students have scored less than 55 marks, find the value u and o. (c) A die is tossed 60 times and the following frequencies are observed. |outcome Observed frequency 12 3 4| 5| 6 4 7 16 8. 8 7 Using a x test, test at 5% level whether the die is fair.
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