Math

QuestionFind the value of CC for a probability distribution where p(0)=0.1p(0)=0.1, p(1)=0.3p(1)=0.3, p(3)=0.2p(3)=0.2, and p(2)=Cp(2)=C such that p(x)=1\sum p(x) = 1.

Studdy Solution

STEP 1

Assumptions1. The values of the random variable are x=0x=0, x=1x=1, x=x=, and x=3x=3 . The corresponding probabilities are p(x=0)=0.1p(x=0)=0.1, p(x=1)=0.3p(x=1)=0.3, p(x=)=Cp(x=)=C, and p(x=3)=0.p(x=3)=0.
3. The sum of all probabilities in a probability distribution equals1

STEP 2

We need to find the value of CC such that the sum of all probabilities equals1. We can do this by setting up an equation and solving for CC.
p(x=0)+p(x=1)+p(x=2)+p(x=)=1p(x=0) + p(x=1) + p(x=2) + p(x=) =1

STEP 3

Now, plug in the given values for the probabilities to set up the equation.
0.1+0.3+C+0.2=10.1 +0.3 + C +0.2 =1

STEP 4

implify the equation by adding the known probabilities.
0.6+C=10.6 + C =1

STEP 5

To solve for CC, subtract0. from both sides of the equation.
C=10.C =1 -0.

STEP 6

Calculate the value of CC.
C=10.6=0.4C =1 -0.6 =0.4So, the value of CC such that the sum of all probabilities equals1 is C=0.4C=0.4.

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