S2) The probability density function fX (x) of the random variable X fX(x) =( 4x3 0 < x ≤ 1 ( 0 otherwise given in the form. P(X ≤2/3|X > 1/3) Find the probability of the event. S3) Using the information given in S2 A = {X > 1/8} conditional probability density function under the condition Find. Find the domain of the function. Describe in detail how you found it. Of x conditionally expected Find the value.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
S2) The
fX(x) =( 4x3 0 < x ≤ 1
( 0 otherwise given in the form.
P(X ≤2/3|X > 1/3) Find the probability of the
S3) Using the information given in S2 A = {X > 1/8} conditional probability density function under the condition Find. Find the domain of the function. Describe in detail how you found it. Of x conditionally expected Find the value.
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