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Univariate Gaussians or normal distributions have a simple representation in that they can be completely described by their mLet px (;u,2) denote the probability density function of a normally distributed variable X with mean u and variance o2. Whatdenote the probability density function of a normally distributed variable X with mean u and variance o As above, let px (r;

Univariate Gaussians or normal distributions have a simple representation in that they can be completely described by their mean and variance. These distributions are particularly useful because of the central limit theorem, which posits that when a large number of independent random variables are added, the distribution of their sum is approximated by a normal distribution. In other words, normal distributions can be applied to most problems Recall the probability density function of the Univariate Gaussian with mean and variance o2. N (4,a2) (2-)2/(2) px (z) /2o2 5. (a) 1 point possible (graded) N (1,2) i.e., the random variable X is normally distributed with mean 1 and variance 2. What is the probability that XE [0.5,2]? Let X (Write a solution with at least 4 decimal places)
Let px (;u,2) denote the probability density function of a normally distributed variable X with mean u and variance o2. What value of maximizes this function? (Use mu to represent the mean and sigma to represent the standard deviation.)
denote the probability density function of a normally distributed variable X with mean u and variance o As above, let px (r; u, a2) What is the maximum value of px (x; u,o2) (Use mu to represent the mean and sigma to represent the standard deviation.)
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5. Ca) . N(,2) 2 2 . H-1 xe [o.5,21 is that 5,2 o.5 2 -(e) 2 TTG 2 -I) 2X2 2 TT 2 O5Let 1-3C At CO.5-)= 2 ズ= 0.5 -o.5 2. (2-1)= 2 du O.707106 2 alu. 2 TT 0. 35355 Normal he intrant distmibutin standord ond Nammmaximum fanetion is The at Value Ghe maximum PM(X=)= 2 2 TTG 2TTG

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