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
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)).
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.