Basics of ML & AL Week 2 Challenge
Q1.
1st Business Moment: Measure of Central Tendency
This moment speaks about the center of the data point and indicates where the majority of data points lie.
a.) Mean:
The average of all the data points in a data set is called the mean.
For Population,
μ = (Σ Xi) / N
here it is nothaving the same probability so we arre using the EX formula
Expected value =(0*0.35+1*0.25+2*0.15+3*0.15+4*0.10)
1.4
provability of zero and 1 is more
Mean= 1.4
b. Median:
The middlemost value when the dataset is sorted in ascending order
0+1+2+3+4
2 is median
c. Mode:
The most repeated values in the dataset is called mode
0,1,2,3,4 all are mode
Mean < median so it is
2nd Business Moment: Measure of Dispersion
This moment describes the spread of data points around the mean. It speaks about how far
the data points are distributed away from the mean.
a. Variance:
It measures the difference between each data points from the mean
For the population,
σ2 = Σ (Xi – μ )2 / N
(4+1+0+1+4)/5 = 2
(0*0.35+1*0.25+2*0.15+3*0.15+4*0.10)
-1.4+
b. Standard deviation:
Square root of the variance refer as standard deviation.
σ = sqrt [ Σ (Xi – μ )2 / N]
Sq(2)
1.4
Range:
The difference between the maximum and the minimum value of the dataset
Range = max value – min value
4-0 =4
3rd Business Moment: Skewness
Mean = mode so it is normal (no squad)
is representing a normal distribution curve without any skewness,
4th Business Moment: Kurtosis
Kurtosis is an estimation of the peak of the curve. It measures if the data is lightly or heavily tailed from the normal curve. A high kurtosis value indicates the presence of outliers.
Mesokurtic represents the shape of our normal curve.
Q2.
Q3.
Skewness < 0 – Left skewed distribution – most values are concentrated on the right of the mean, with extreme values to the left.
Nithor good or bad
mean of the returns is negative, it means that overall performance is negative, but the outlier months are positive. A negative skew is generally not good, because it highlights the risk of left tail events .While a consistent and steady track record with a positive mean would be a great thing, if the track record has a negative skew then you should proceed with caution.
Q4.
mean = 680
standard deviation = 31
- Calculate Z-score corresponding to x- mean/sd (710-680)/310.96
- Calculate the probabilities using Z-tables, P(Z < 0.96) =
P(x<Z) = 0.83147
P(X>740)
0.16853
P(600<X<720)
0.33147
P(X=720)
720-680/31
Q5.
given graph is normaly distriuted .
The normal distribution is a continuous probability distribution that is symmetrical on both sides of the mean, so the right side of the center is a mirror image of the left side..
This means there is a 68.2% probability of randomly selecting a score between -1 and +1 standard deviations from the mean
Right side is divided into 3 qurtiles
34.2 0 to +1
13.6 1 to 2
remaining 2 to 3
if we wantto find exact area the using ztable we can find it
full z- Positive/nigative z = intercetion z value We get
Q1.
1st Business Moment: Measure of Central Tendency
This moment speaks about the center of the data point and indicates where the majority of data points lie.
a.) Mean:
The average of all the data points in a data set is called the mean.
For Population,
μ = (Σ Xi) / N
here it is nothaving the same probability so we arre using the EX formula
Expected value =(0*0.35+1*0.25+2*0.15+3*0.15+4*0.10)
1.4
Mean= 1.4
b. Median:
The middlemost value when the dataset is sorted in ascending order
0.30 is median
(0*0.35+1*0.25+2*0.15+3*0.15+4*0.10)
0,0.25,0.30,0.45,0.40
c. Mode:
The most repeated values in the dataset is called mode
0,0.25,0.30,0.45,0.40 all are mode
mode<mean
is a positively skewed curve having the mass on the left side of the curve and a long tail extending towards the left side of the curve.
2nd Business Moment: Measure of Dispersion
This moment describes the spread of data points around the mean. It speaks about how far
the data points are distributed away from the mean.
a. Variance:
It measures the difference between each data points from the mean
For the population,
σ2 = Σ (Xi – μ )2 / N
(0-1.4)2+(0.25-1.4)2+(0.30-1.4)2+(0.45-1.4)2+(0.40-1.4)2/5 = 2
(1.96+1.21+1.3+0.90+1)/5
1.27
b. Standard deviation:
Square root of the variance refer as standard deviation.
σ = sqrt [ Σ (Xi – μ )2 / N]
Sq(1.27)
1.1
Range:
The difference between the maximum and the minimum value of the dataset
Range = max value – min value
0.45-0 =0.45
3rd Business Moment: Skewness
mode<mean
is a positively skewed curve having the mass on the left side of the curve and a long tail extending towards the left side of the curve.
4th Business Moment: Kurtosis
Kurtosis is an estimation of the peak of the curve. It measures if the data is lightly or heavily tailed from the normal curve. A high kurtosis value indicates the presence of outliers.
In the Leptokurtic curve, kurtosis has a positive value
Q2.
The expectation or expected value of a random variable is a single number that tells us a lot about the behavior of the variable. Roughly, the expectation is the average value of the random variable where each value is weighted according to its probability.
Expected value is the average value of a random variable over a large number of experiments. A random variable maps numeric values to each possible outcome in an experiment. We can calculate expected value for a discrete random variable
General arithmetic mean formula = {Sum of Observation}÷{Total numbers of Observations}.
A probability distribution tells us the probability that a random variable takes on certain values.
We typically calculate the mean after we’ve actually collected raw data.
Q3.
Skewness < 0 – Left skewed distribution – most values are concentrated on the right of the mean, with extreme values to the left.
mean of the returns is negative, it means that overall performance is negative, but the outlier months are positive. A negative skew is generally not good, because it highlights the risk of left tail events .While a consistent and steady track record with a positive mean would be a great thing, if the track record has a negative skew then you should proceed with caution.
Q4.
mean = 680
standard deviation = 31
1/1+e^-z
nom()
- Calculate Z-score corresponding to x- mean/sd (710-680)/310.96
- Calculate the probabilities using Z-tables, P(Z < 0.96) =
P(x<Z) = 0.83147
P(X<711)
zscore =1
P(x<711) = 0.84134
P(X>740)
zscore 1.9
P-value from Z-Table:
P(x<740) = 0.97353
P(x>740) = 1 - P(x<740) = 0.026465
P(680<x<740) = P(x<740) - 0.5 = 0.47353
P(600<X<720)
zscore=3.87097
P(x<720) = 0.99995
P(x>720) = 1 - P(x<720) = 0.00005
P(600<x<720) = P(x<720) - 0.5 = 0.49995
P(X=720)
zscroe=1.29032
P-value from Z-Table:
P(x<720) = 0.90153
P(x>720) = 1 - P(x<720) = 0.098469
P(680<x<720) = P(x<720) - 0.5 = 0.40153
Q5.
given graph is normaly distriuted .
The normal distribution is a continuous probability distribution that is symmetrical on both sides of the mean, so the right side of the center is a mirror image of the left side..
This means there is a 68.2% probability of randomly selecting a score between -1 and +1 standard deviations from the mean
Right side is divided into 3 qurtiles
34.2 0 to +1
13.6 1 to 2
remaining 2 to 3
if we wantto find exact area the using ztable we can find it
full z- Positive/nigative z = intercetion z value We get