School Commit Init

2024-08-31 12:07:21 +03:00
commit 0b130ee18c
2801 changed files with 4720552 additions and 0 deletions
@@ -0,0 +1,48 @@
+# X ~ Bino(3,0.5)
+
+# We are solving Application from lab 2
+
+n=3 # 3 coin flips
+p=0.5 # coin flips <=> 0.5 probability
+
+x=0:1:n;
+px=binopdf(x,n,p);
+#   ( 0    1   2   3 )
+# X ( 1/8 3/8 3/8 1/8)
+#
+plot(x,px,"+");
+hold on
+
+# P(X=0) = binopdf(0,3,0.5) =1/8
+p1=binopdf(0,3,0.5);
+printf('P(X=0)=%1.6f\n',p1)
+
+xx=0:0.01:n;
+
+
+# P(X!=0) = 1 - binopdf(1,3,0.5) =5/8
+p2=1-binopdf(1,3,0.5); # PROBABILITY OF THE COMPLAMENTARY EVENT
+printf('P(X!=0)=%1.6f\n',p2)
+
+#P(X<=2) = binocdf(2,3,0.5) = 7/8
+p3=binocdf(2,3,0.5);
+printf('P(X<=2)=%1.6f\n',p3)
+
+#P(X<2) = binocdf(1,3,0.5) = 1/2 P(X<2)=P(X<=1)
+p4=binocdf(1,3,0.5)
+printf('P(X<2)=%1.6f\n',p4)
+
+# P(X>=1) = 1-P(X<1) = 1 - binocdf(0,3,0.5)
+p5=1 - binocdf(0,3,0.5); # PROBABILITY OF THE COMPLAMENTARY EVENT
+printf('P(X>=1)=%1.6f\n',p5)
+
+# P(X>1) = 1 - P(X<=1) - binocdf(1,3,0.5)
+p6=1 - binocdf(1,3,0.5); # PROBABILITY OF THE COMPLAMENTARY EVENT
+printf('P(X>1)=%1.6f\n',p6)
+
+N=input("Give the number of simulations N=");
+U=rand(3,N); # Generate N simulations of 3 coin tosses
+Y=(U>0.5);  # Transforms decimal in True for Heads(>0.5) or False for Tails
+X=sum(Y);   # Sums up the collums
+clf         # Clear the figure
+hist(X);    # Plots X