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The Lognormal Distribution
If ln(X) is a normally distributed random variable, then X is said to be a lognormal variable.
If P1, P2, P3, ... are the prices of a scrip in periods 1, 2, 3, ..., some applications in finance require ln (P2/P1), ln (P3/P2),... to be normally distributed, that is, continuously compounded returns are required to be normal. This property is described as “Stock Prices are Lognormal”.
REMARK
The previous random variables arose out of natural experiments. The following distributions are derived distributions. That is, it is a function of other distributions. We require the following two distributions in Testing of Hypothesis. and our presentation will be restricted by our requirements.
Convert each of the following points into the specified coordinate system. (a) (-4, 2 Π /3) into Cartesian coordinates. (b) (-1,-1) into polar coordinates. Solution
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
What percent of the figure below is shaded? Break the rectangle into eighths as shown below. The shaded part is 6/8 or 3/4 ; 3/4 is 75%.
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Ask question #Minimum 100 words accepted what is a ratio
Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1)
E1) How is the 'comparison model' different from the 'complementary addition model'? E2) Create one word problem related to the children's world for each of the 4 models liste
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Determine the fundamental period of the following discrete-time signal: X(n) = 2sin(4n)π +π/4) + 5sin16n +4sin (20n +π/3)
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