Thread: Help me to solve this probability question

If the discrete random variable X is the number of heads obtained in four tosses of a fair coin.Find the probability distribution of X.Hence,tabulate the probability distribution of Y=1/1+2x.Please me to solve this..thank u

Hey sharmala.

Is this distribution Y = 1/(1+2X) instead of Y = 1 + 2X?

In any case, you have a distribution for all X belonging to all whole numbers from 0 to 4 inclusive. Now consider that Y = f(X) with the same probabilities for each value of X. So you should have a table with three rows: one is the probability, the second is P(X = x) and the final one is P(Y = y) or P(Y = f(x)).

Can I get more explanation....please

In any distribution you have a Probability Mass Function P(X = x) for every possible x and you also have the x that corresponds to it. As an example, consider a simple Bernoulli distribution with p = 1/2:

P(X = 0) = 1/2 for X = 0
P(X = 1) = 1/2 for X = 1.

Now I will do a simple transformation where Y = (1+X)^2 = f(X). This gives

P(Y = f(0)) = 1/2 for Y = f(0) = (1+0)^2 = 1
P(Y = f(1)) = 1/2 for Y = f(1) = (1+1)^2 = 4 so we have a distribution of Y which looks like:

P(Y = 1) = 1/2
P(Y = 4) = 1/2.