Finding out the probability distribution of numbers from -3 to 3

Question

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a big thanks to every one..

Please explain this problem..

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A random variable 'X' takes the values -3,-2,-1,0,1,2,3. Such that P(X=0) = P(X<0) = P(X>0) and P(X=-3) = P(X=-2) = P(X=-1) and P(X=3) = P(X=2) = P(X=1). Obtain the distribution of X.

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I have found that P(X=0) = 1/7; and now how to proceed...

Answer 1

You've found it incorrectly. The first condition tells us that $$ P(X = 0) = P(X > 0) = P(X < 0) =\frac13 $$ since the sum of these three probabilities is $1$. For other $6$ points, probabilities are $\frac19$.

Answer 2

Hint

Set $p_{-3}=p_{-2}=p_{-1}=a$ and $p_{3}=p_{2}=p_{1}=b$ then:

$$3a+p_{0}+3b=1$$

$$3a=p_{0}=3b$$