18. The probability distribution functions which shows the number of hours (X) a student study during
lockdown period in a day, is given by (where C>0)
0
1
2
P(X) 3C 4C - 10C2 5C-1
On the basis of above information answer the following questions:
(i) The correct equation for C is
(a) 303 - 10C2 + C -2 = () (b) 303 + 10C2+C – 2 = 0
(c) 3C - 10C2 + 9C – 2 = 0 (d) None of these
(ii) The value of C is
1
2
(b)
(cÀ
(d)
3
6
(iii) P(X<2) -
1
2
(a)
(b)
(c)
()
3
4
(iv) P(X = 1) =
2
I
2
(b
)
(a)
(a)
(v) P(X 20) =
1
(a)
2
(b)
b
(c) 1
(d) 0
Answers
Answered by
0
Answer:
We must have ∑P(X)=1
⇒P(X=0)+P(X=1)+P(X=2)=1
⇒(3C
3
)+(4C−10C
2
)+(5C−1)=1
⇒3C
3
−10C
2
+9C−2=0
⇒(C−1)(3C
2
−7C+2)=0
⇒(C−1)(C−2)(3C−1)=0
⇒C=1,2,
3
1
Also 0≤P(X=0),P(X=1),P(X=2)≤1
So only acceptable value of C is
3
1
(ii) P(X<1)=P(X=0)=3(
3
1
)
3
=
9
1
(iii) P(1<X≤2)=P(X=2)=4C−10C
2
=4⋅
3
1
−10⋅
9
1
=
9
2
and
P(0<X≤3)=1−P(X=0)=1−
9
1
=
9
8
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