Question

score on last try: 0.75 of 1 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorrect part. > next question get a similar question you can retry this question below let x be a random variable whose pdf is given by the plot below. assume that the pdf is zero outside of the interval given in the plot. estimate the mean of x. estimate the standard deviation of x to within 0.5. for which a is p(a ≤ x ≤ a + 2) maximized? estimate p(0 ≤ x ≤ 2) to two decimal places. submit question

Explanation:

Step1: Recall probability from pdf

The probability $P(0\leq X\leq 2)$ is the area under the probability - density function (pdf) curve from $x = 0$ to $x = 2$. Since the total area under the pdf curve is 1, and for a symmetric - like distribution (the given pdf seems approximately symmetric about $x = 1$), we can estimate the area by visual inspection.

Step2: Visual estimate

The area under the curve from $x = 0$ to $x = 2$ seems to be about 0.35. We can think of it in terms of the proportion of the total area under the curve. The distribution is centered around $x = 1$, and the interval $[0,2]$ captures a significant part of the "hump" of the distribution.

Answer:

0.35