If you vertically compress the absolute value patent function, f(x)=|x|, by a factor of 5, what is the equation of the new funct
ion?
1 answer:
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Answer:
Step-by-step explanation:
A uniform distribution, "sometimes also known as a rectangular distribution, is a distribution that has constant probability".
We need to take in count that our random variable just take values between 0 and 1 since is uniform distribution (0,1). The maximum of the finite set of elements in (0,1) needs to be present in (0,1).
If we select a value we want this:
And we can express this like that:
for each possible i
We assume that the random variable are independent and
from the definition of an uniform random variable between 0 and 1. So we can find the cumulative distribution like this:
And then cumulative distribution would be expressed like this:
For each value we can find the dendity function like this:
So then we have the pdf defined, and given by:
and 0 for other case
And now we can find the expected value for the random variable X like this:
Answer:
21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Calculate the probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
This is 1 subtracted by the pvalue of Z when X = 9.08. So
has a pvalue of 0.7823
1 - 0.7823 = 0.2177
21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.