35. Chebychey's Theorem Old Faithful is a famous geyser at Yellowstone National Park. From a sample with 32. the mean duration o
f Old Faithful's eruptions is 3.32 minutes and the standard deviation is 1.09 minutes. Using Chebycher's Theorem, determine at least how many of the eruptions lasted between 1.14 minutes and 5.5 minutes. (Source: Yellowstone National D 36. Chebycher's Theorem The - 577
1 answer:
Answer:
The probability that the eruptions lasted between 1.14 min and 5.5 minutes is greater than 75%
Step-by-step explanation:
The explanation can be found in the attached picture. Chebyshev's <u>inequality </u>was used. It predicts the probability of the random variable to be in ( mean- K* standard dev< x < mean + K*standard dev).
Note: K must be greater than 1
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Answer:
Step-by-step explanation:
Given
a)
we know that
therefore
on integrating we get
c=(1/6640)
b)
on doing the integration we get
=0.37349
c)
marginal density of X is
on doing integration we get
f(x)=(4x+3)/3320 ; 0<x<40
marginal density of Y is
on doing integration we get
d)
solve the above integration we get the answer
e)
solve the above integration we get the answer
f)
Two variables are said to be independent if there jointprobability density function is equal to the product of theirmarginal density functions.
we know f(x,y)
In the (c) bit we got f(x) and f(y)
f(x,y)cramster-equation-2006112927536330036287f(x).f(y)
therefore X and Y are not independent