Question

For the probability distribution, if P(X)=C(1/4)^x, X=1,2,3, then C=​

Answer 1

Answer:

(i) We must have ∑P(X)=1

⇒P(X=0)+P(X=1)+P(X=2)=1

⇒(3C3)+(4C−10C2)+(5C−1)=1

⇒3C3−10C2+9C−2=0

⇒(C−1)(3C2−7C+2)=0

⇒(C−1)(C−2)(3C−1)=0

⇒C=1,2,31

Also 0≤P(X=0),P(X=1),P(X=2)≤1

So only acceptable value of C is 31

(ii) P(X<1)=P(X=0)=3(31)3=91

(iii) P(1<X≤2)=P(X=2)=4C−10C2=4⋅

Answer 2

Answer:

64/21

Step-by-step explanation:

We know that, ∑P(X) = 1

$=> P(X) = c [(\frac{1}{4})+(\frac{1}{4})^2+(\frac{1}{4})^3 ]\\\\=> P(X) = c [\frac{1}{4} + \frac{1}{16} +\frac{1}{64} ]\\\\=> 1 = c(\frac{16 + 4 + 1}{64} )\\\\=> 1 = c (\frac{21}{64} )\\\\=> c = \frac{64}{21}$

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