A continuous random variable X has a PDF f(x)= 3x²,0 a} and (ii) P{X >b} = 0.05.
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- Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?A particular pumping engine will only function properly if an essential component functions properly. The time to failure of the component ( in thousands of hours) is a random variable X with probability density f(x) = 0.02xe-0.01x^2 for x > 0. What is the proportion of pumping engines that will not fail before 10,000 hours of use? What is the probability that the engine will survive for another 5000 hours, given that it has functioned properly during the past 5000 hours?If Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value of the PDF between 4 and 10 is?
