Problem 2: (Points 40) A Gaussian random voltage has a mean value 5 and a varian

Question

Problem 2: (Points 40) A Gaussian random voltage has a mean value 5 and a variance 16. Find the mean value? (c) Find the third central moment of the voltage d) Find the third moment of the voltage (a) The probability that an observed value of the voltage is greater than zero? (b) What is the probability that an observed value of the voltage is greater than zero but less than or equal to (x ) as 000102 03 04 06 07 08 9 5000 5040 s080 5120 5160 5199 5239 5279 5319 5359 5398 5438 5478 5517 5557 596 5636 5675 5714 5753 0.2 .5793 .5832 .5871 5910 5948 .5987 .6026 6064 .6103 6141 0.3 .6179 .6217 ,6255 .6293 .6331 6368 bas sus .6480 AS17 04 6554 6591 6628 6664 6700 6736 6772 6808 6844 6879 0.5 6915 6950 .6985 7019 7os4 7088 7123 7157 .7190 7224 06 7257 7291 7324 7357 7389 7422 7454 7486 7517 7549 0.7 7sso 7611 .7642 .7673 .7704 7734 .7764 7794 .7823 .7852 08 7881 .7910 .7939 .7967 .7995 .8023 8051 3078 Si06 H33 8389 1.2 8849 .8869 .8888 .8907 .8925-8944 8962 8980 ,8997 9015 9032 9099 911S 9131 9147 9162 917 92 18 25 16 92 94 95 96 // 93 94 95 86 38

Explanation / Answer

Gaussian Random Voltage would be normally distributed :

a) 0 is 0 - 5 = -5 away from the mean, which is -5/16 = -0.3125 times the standard deviation. This is our z-statistic.

P( Obs. voltage > 0 )
= P( z > z-statistic )
= 1 - P(z < z-statistic)
= 0.62267
= 62.27%

b) 1 is 1 - 5 = -4 away from the mean, which is -4/16 = -0.25 times the standard deviation

P( 0 < Obs. voltage < 1)
= P(Obs voltage < 1) - P (Obs voltage < 1)
= P (z < -0,25) - P(z < -0.3125)
= 0.02396
= 2.396%

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