Question

1. Discuss the importance of Normal Distribution in Data Science with one or two applications?
2. Find the mean and variance of Normal Distribution

Answer 1

Note that, Iss Pud. F of. Non dy lond 12= 0 [ 1950, since the integrond Ye 912 is odd function 1 .: E(X) = ll * (1) to all Meg7) = F(X) = ДА Uadionce v (X)= E EX- EXX]]= E(X-412 il CO =s (X-41)? fcx) dze (X-U) 2 202 Οκ Sex-M12 JS 27 o Put y=x-u x = utty dx = ody co -4% 92. X 0 24 2 y elody - 92 schot 202 s 4 e dy - VITT o en T2T [ 1312 2(1) 12 integaand is even function] a = 1/2, b=3 farb 2 (a) alb 021 I SIT 252 02 2 TT variance -V(X)=0?

9.1) Importance of Noomal distoibution in Bata Science Noomal distoibution was fix6t of all discovered by Foench mathematician Abraham Demoiuse in 1733 as an appooximati to binomial distribution for laoge n. the normal distaibution is also called as Gaussian distribution Noomal distribution fiost osed in data Science to cheack normality of the data. This basically means, that if youo data is not normally distaibuted, you need to be very careful what statistical tests you apply to it since they could lead to wrong conclusion, Normal distoibution is ubiquitous because a dataset with finite variance tuons into normal as long as data set with independant feature probabilites is allowed to goota in size. Application: 0 The voglable such as intelligence quotient, height of person, weight of person, poloos in measuoment of Physical quantities follow noomal distribution Normal disaibution is useful in statistical quality control, Etatistical infeconie, seliability theory, oprotion research, educational and psychological statistics, i @ Data sets with roomal disth makes applicable to vadiety of methods that fall under paramedic Statistics The methods such as propagation of on teatainty and leasti squares parameteo fitting that make a data-scientot life easy are applicable only to datasets with moomal og normal like distribution.com

11uYHRHUDU 0.22 Find Mean and anance of noomal distoibution- A continous 8 V X is said to follow noomal distaibution with paoame1896 and 0.2 if its Pdif is, (X-402 for): I e. ; - : - <X60 (UC Ο 21η oro - O Mean: -I 2(x-1) e Eix) = 5x for) dx = ( x Y = X-U we get, dx = o dy ..X= Mtoy 0 -979 912 sdy e E(X) = su tog - สง 21 co y eh dy o e 12 dy & S JET = US DITO te dy -00 Il +12