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8 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Continuous r.v |
If cdf F_X(x) is differentiable, Xis continuous |
cdf |
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Probability Density Function |
Derivative F'_X(x) = f_X(x) |
derivative |
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Properties of p.d.f. |
» f(x) >= 0 » P{a < X < b} = integral_{a,b} f(x) dx » integral_{R} f(x) dx = 1 |
non-negativity probability main feature |
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Expected value of continuous r.v |
Integral_{R} x · f(x) provided that integral_{R} (x · f(x)) |
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E(g(x)) |
Integral_{R} f(x)·g(x) |
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Standard Normal distribution |
N(0,1)
When continuous rv has p.d.f. f(x) = e^{ x^2 / 2 } / (2·pi)^{ 1/2 }
also called Gaussian
E(X) = 0 (as pdf is even and integral{R} f(x)= 1)
Var(X)=1 (as ... = E(X^2)-0 = 1 |
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E(aX+b) |
a·E(X) + b |
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Properties of Continuous r.v-s |
If X~N( mu, sigma^2 ) and Y=aX+b: Y~N( a·mu+b, (a·sigma)^2 ) |
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