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CT8-S2008-Q1b
- Thread starter Jia Syuen
- Start date
Hi Jia
The solution is calculated using the formula for the downside semi-variance (DSV) on the summary page of Chapter 4.
For example, for the Poisson distribution, we are trying to work out DSV(0.02X) where X is Poi(3). I have converted from percentage to decimal to avoid any confusion from the %).
DSV(0.02X) = 0.0004 DSV(X) as the multiplicative constant gets squared in a variance formula.
To work out DSV(X), we use the formula on Page 23 of Chapter 4 for the discrete DSV:
DSV(X) = Σ (x - μ)^2 * P(X = x) where we are summing for x < μ
We have μ = 3 for the Poisson distribution in question so we need to include x = 0, x = 1, x = 2 in the summation.
Hence the summation becomes:
(0 - 3)^2 * P(X = 0) + (1 - 3)^2 * P(X = 1) + (2 - 3)^2 * P(X = 2)
Now substitute in for the Poisson probabilities using the probability function on Page 7 of the Yellow Tables.
Does this give you enough info to have a go Jia? Remember to multiply by the 0.0004 at the end to get DSV(0.02X).
All the best
Anna
The solution is calculated using the formula for the downside semi-variance (DSV) on the summary page of Chapter 4.
For example, for the Poisson distribution, we are trying to work out DSV(0.02X) where X is Poi(3). I have converted from percentage to decimal to avoid any confusion from the %).
DSV(0.02X) = 0.0004 DSV(X) as the multiplicative constant gets squared in a variance formula.
To work out DSV(X), we use the formula on Page 23 of Chapter 4 for the discrete DSV:
DSV(X) = Σ (x - μ)^2 * P(X = x) where we are summing for x < μ
We have μ = 3 for the Poisson distribution in question so we need to include x = 0, x = 1, x = 2 in the summation.
Hence the summation becomes:
(0 - 3)^2 * P(X = 0) + (1 - 3)^2 * P(X = 1) + (2 - 3)^2 * P(X = 2)
Now substitute in for the Poisson probabilities using the probability function on Page 7 of the Yellow Tables.
Does this give you enough info to have a go Jia? Remember to multiply by the 0.0004 at the end to get DSV(0.02X).
All the best
Anna