Answer:
a) P(X=x) = p× (1-p)^(x-1)
b) P(X=3) = 0.081
c) P(X≤5) = 0.40951
d) Mean of X= 10
e) Var(X)= 90
Step-by-step explanation:
This is a question on geometric distribution.
In geometric distribution, we have two possible outcomes for each trial (success or failure) for independent number of binomials series trial. Also the probability of success is constant for each trial.
This discrete probability distribution is represented by the probability density function: f(x) = p× (1-p)^(x-1)
For a random variable with a geometric distribution, we do not know the number of trials we will have = {1, 2, 3, ...}
We stop the trials when we get a success.
From the question, there are 10 numbers
The probability of success = p = 1/10
For the solutions of the question from (a-e), See attachment below.
f(x) = P(X= x)
Where P(X= x) is the probability of X taking on a value x
