Q The random variable X can take only the values 0, l, 2 and 3 Given that - Maths - Probability

Question

Q The random variable X can take only the values 0, l, 2 and 3
Given that
P(X=0) =P(X=1)= p and
P(X=2)=P(X=3) such that ∑ p i x i 2   =
2 ∑ p i x i , find the value of p

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

PX=0=PX=1=pLet Px=2=PX=3=aNow,PX=0+PX=1+PX=2+PX=3=1p+p+a+a=12p+2a=1   
 1∑pixi2=02p+12p+22a+32a=p+4a+9a=p+13a∑pixi=0p+1p+2a+3a=p+5aAs ∑pixi2 = 2 ∑pixip+13a = 2 p+5ap + 13a = 2p+10ap=3aSubstituting the value of p in 1 , we get6a+2a=18a=1a=18p=38   ANS
Hope this information will clear your doubts about the topic
If you have any more doubts just ask here on the forum and our
experts will try to help you out as soon as possible

Regards

Q. The random variable X can take only the values 0, l, 2 and 3. Given that P(X=0) =P(X=1)= p and P(X=2)=P(X=3) such that ∑ p i x i 2 = 2 ∑ p i x i , find the value of p.

Q. The random variable X can take only the values 0, l, 2 and 3. Given that
P(X=0) =P(X=1)= p and P(X=2)=P(X=3) such that $\sum_{} p_{i} {x_{i}}^{2} = 2 \sum_{} p_{i} x_{i}$ , find the value of p.