The random variable x has the following probability distribution: 
a.Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b.Calculate the expected value of x.
c.Calculate the variance of x.
d.Calculate the standard deviation of x.
Definitions:
Operant Behavior
Behavior emitted spontaneously or voluntarily that operates on the environment to change it.
Respondent Behavior
Reactions that are automatic and involuntary, typically elicited by specific stimuli, contrasted with operant behavior, which is influenced by its consequences.
Extinguishable Behavior
A learned response that decreases in frequency or disappears when it is no longer reinforced in a behavioral psychology context.
Fixed-Interval
A schedule in operant conditioning where rewards (reinforcements) are given at fixed times, provided the correct response is made.
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