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Question 4 (2 points) Let X ~ NZ 4) where 4 is the variance of X Then find the 3rd percentile of the of this random variable0.52323.2384Not enough information:9.165...

Question

Question 4 (2 points) Let X ~ NZ 4) where 4 is the variance of X Then find the 3rd percentile of the of this random variable0.52323.2384Not enough information:9.1656

Question 4 (2 points) Let X ~ NZ 4) where 4 is the variance of X Then find the 3rd percentile of the of this random variable 0.5232 3.2384 Not enough information: 9.1656



Answers

Find the mean, variance, and standard deviation of the random variable $x$ associated with the probability density function over the indicated interval. $$f(x)=\frac{4}{3 x^{2}} ;[1,4]$$

Yeah. This problem we were told that sigma squared for X is fine Insert required for why is three. We would like to find the variance of the random variable dizzy. Doesn't mean you have to acts plus four. Why minus three? The variance of the it was a variance of negative two X plus four Y minus three. Yeah. Which using our themes from the book is the same as two squared times the variance effect Most four square in terms of variants of why. And then that constant on the end does not change the variance. And so we know the variance of that Is five. So this is four times 5 16 times of variants of Y which we know to be three. So this is 20 plus 48 Which is 68. It's our variants of Z is 68.

We have a normal distribution with mean three and standard deviation 0.25 We want to find the probability given this normal distribution that X is greater than or equal to to to solve this problem, we're gonna thank not. In terms of X. In terms of Z scores, which made normal distributions easier to understand specifically with regards to area and probability to start remember that a Z score by definition is equal to X minus the mean, divided by the standard deviation. So we can convert our bounds of extra than equal to to to a Z score as follows, two minus 32 by the by 0.25 is equal to negative four. With this in hand, we can now re express this problem as the probability Z is gooder than or equal to negative four or one minus the probability that Z is less than or equal to negative. For putting it in the notation on the right allows us to use a Z look up table which will exactly give us an answer for the value of P of z less than or equals negative four. Doing so, we obtain one minus 0.3 giving us our final solution of 0.99997

We have a normal distribution with mean three and standard deviation 0.25 We want to find the probability given this normal distribution that X is greater than or equal to to to solve this problem, we're gonna thank not. In terms of X. In terms of Z scores, which made normal distributions easier to understand specifically with regards to area and probability to start remember that a Z score by definition is equal to X minus the mean, divided by the standard deviation. So we can convert our bounds of extra than equal to to to a Z score as follows, two minus 32 by the by 0.25 is equal to negative four. With this in hand, we can now re express this problem as the probability Z is gooder than or equal to negative four or one minus the probability that Z is less than or equal to negative. For putting it in the notation on the right allows us to use a Z look up table which will exactly give us an answer for the value of P of z less than or equals negative four. Doing so, we obtain one minus 0.3 giving us our final solution of 0.99997

This problem, it is given that the random variable X is equally likely to assume any of the values one by eight, one by four. Our three x 8 X can assume any of the values one x 8, one x 4 or three x 8 and it is equally likely to assume any value. We have to determine the mean and variance of X. We know that there never a simple space consists of and possible outcomes that are equally likely. The probability of each outcome is one by n. Here, X Is equally likely to a jew three values. That is one x 8, one x 4 and three x 8. So the probability of each outcome will be won by three. That is for each X. It's probability fx baby, one by three. Cool one, battery And one x 3 for x equal to one x 8. one x 4 or three x 8. The probability for each value of X is one x 3. So that the total probability will be one. Now we have to determine its me and variance. We know that me mu which is equal to expected X is the sum of all X into effects over all eggs. So it will be one x 8 into one x 3 plus one by four into one by three plus three by eight into one by three. one x 8 into one x 3 is one divided by 24 plus one x 4 into one x 3 is one divided by 12 plus three x 8 in 2, 1 x three is 1 x eight. So one by 24 plus one by 12 plus one by eight. This is equal to The common denominator will be 24 and in the numerator we have fun last two plus three. This is equal to six, Divided by 24 and 6.24 is equal to one by four. So mean that this expected X is one x 4. Now we will find variants variance, sigma squared is equal to submission over all. X X square effects minus mu square that is minus mean square first. We will find submission overall. Next X squared Ethics. This is equal to one by eight square in 21 by three plus one by four square in 21 by three plus three by eight square in 21 by three. So this is equal to one by eight. Square is one by 64 In 2, 1 x three plus one x 4 square is one x 16 In 2, 1 x three less three x 8 square is nine divided by 64 In 2, 1 x three. This is equal to one x 92, one x 192, 64 into three is 1 92. So one by 1 92 Plus 16 into three is 48. So one x 48. Yes, here three ones are three and three threes are nine. So plus three x 64, one by 1 92 plus one by 48 plus three by 64. Now we have to add these three fractions. The common denominator here will be 192. And in the numerator we have what? Plus four Plus three, threes are nine so 9. This is equal to certain, Divided by 1 92. 14 divided by 192 is equal to seven Divided by 96. So some mission. Overall, eggs exclude effects is seven x 96. Sigma square is equal to This submission that is seven divided by 96 minus square of the me. That is square off one by four Square off one x 4 is one x 16. So this is equal to in the denominator we have 96, And in the numerator we have 7 -6, So variance is equal to one x 96. That is one x 96, which is equal to zero point 01 04, So variance is equal to 0.0104, Me is equal to one x 4, and variance is equal to 0.0104.


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