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Answer:
a)
X | 1 3 5 7
f(X) | 0.4 0.2 0.2 0.2
b)
Step-by-step explanation:
For this case we have defined the cumulative distribution function like this:
And we know that the general definition for the distribution function is given by:
Where f represent the density function.
Part a
For this case we need to find the density function, so we can find the values for the density for each value of X = 1,2,3,4,5,6,7,... since X is a discrete random variable.
And for any value higher than 7 we have that:
So then we have our density function defined like this:
X | 1 3 5 7
f(X) | 0.4 0.2 0.2 0.2
Part b
For this case we want to find this probability
And since the random variable is discrete we can write this like that: