Basics of ML & AL Week 2 Challenge

Ans 2. In case of infinite number of Observations, it is very difficult to note each and every outcome. In such cases the probability of each outcome is determined using this probability. The formula is :

μ=∑x⋅P(x)${\displaystyle \mu =\sum x\cdot P\left(x\right)}$

Simple Mean : In case of Finite number of Observations the sample mean is calculated by (Sum of all observations/number of observations) .

Ans 3. Skeness: It is a measure of asymmetry of the probability density function of a real-valued andom variable about its mean.

Having skewness in the curve is not considered to be bad in the analysis, Skewness is the attribute to describe the distribution.

Ans 4. z-score z = (X - μ) / σ

a) P(X < 711)

z = (711 - 680) / 31 = 1

P(X < 711) = P(Z < 1) = 0.8413 (using z-table or calculator)

b) P(X > 740)

z = (740 - 680) / 31 = 2

P(X > 740) = P(Z > 2) = 1 - P(Z ≤ 2) = 1 - 0.9772 = 0.0228

c) P(600 < X < 720)

First, find z-scores for 600 and 720:

z1 = (600 - 680) / 31 = -2.58

z2 = (720 - 680) / 31 = 1.29

P(600 < X < 720) = P(-2.58 < Z < 1.29) = P(Z < 1.29) - P(Z < -2.58) = 0.9015 - 0.0049 = 0.8966

d) P(X = 720)

In a continuous distribution, the probability of a single value is zero, since the area under the curve at a single point is zero.

P(X = 720) = 0

Ans 5. We consider the standard deviation of the data is σ then,

68.2% (34.1 + 34.1) of the data will lie between (μ−1σ)${\displaystyle (\mu -1\sigma )}$ to (μ+1σ)${\displaystyle (\mu +1\sigma )}$

95.4% (47.7 + 47.7) of the data will lie between (μ−2σ)${\displaystyle (\mu -2\sigma )}$ to (μ+2σ)${\displaystyle (\mu +2\sigma )}$

99.7% (49.85 + 49.85) of the data will lie between (μ−3σ)${\displaystyle (\mu -3\sigma )}$ to (μ+3σ)${\displaystyle (\mu +3\sigma )}$.