/*********************************************************************************/ /***** syntax to calculate probabilities from the binomial distribution***********/ /*1. Let X~Bin(n, p) with x={0,1,2,3,…,n} then P(X=x)= PDF('binomial', x, p, n) */ /*2. Let X~Bin(n, p) with x={0,1,2,3,…,n} then P(X<=x)=probbnml(p, n, x) */ /*3. Let X~Bin(n, p) with x={0,1,2,3,…,n} then P(X<=x)=CDF(‘binomial’, x, p, n) */ /*4. Let X~Bin(n, p) with x={0,1,2,3,…,n} then P(X>x)=SDF(‘binomial’, x, p, n) */ /**********************************************************************************/ data Q1_1; prob1_a= PDF('binomial',13,0.65,20); prob1_b = probbnml(0.65, 20, 13)- probbnml(0.65, 20, 12); prob1_c= CDF('binomial', 13, 0.65, 20)- CDF('binomial', 12, 0.65, 20); run; proc print data=Q1_1; run; data Q1_2; prob2_a = probbnml(0.65, 20, 13); prob2_b= CDF('binomial', 13, 0.65, 20); run; proc print data=Q1_2; run; data Q1_3; prob3_a = 1 - probbnml(0.65, 20, 12); prob3_b= 1- CDF('binomial', 12, 0.65, 20); prob3_c=SDF('binomial',12,.65,20); run; proc print data=Q1_3; run; data Q1_4; prob4_a = 1 - probbnml(0.65, 20, 13); prob4_b= 1- CDF('binomial', 13, 0.65, 20); prob4_c=SDF('binomial',13,.65,20); run; proc print data=Q1_4; run; data Q1_5; prob5_a = probbnml(0.65, 20, 12); prob5_b= CDF('binomial', 12, 0.65, 20); run; proc print data=Q1_5; run; data Q1_6; prob6_a= PDF('binomial',8,0.65,20)+ PDF('binomial',9,0.65,20)+ PDF('binomial',10,0.65,20); prob6_b = probbnml(0.65, 20, 10)- probbnml(0.65, 20, 7); prob6_c= CDF('binomial', 10, 0.65, 20)- CDF('binomial', 7, 0.65, 20); run; proc print data=Q1_6; run; /************************************************************************************************/ /***** syntax to calculate probabilities from the normal distribution****************************/ /*1. Let Z~N(0, 1) then P(Z<=z)= probnorm(z) OR P(Z<=z)= CDF('normal', z) */ /*2. Let X~N(µ, s) then P(X<=x)= probnorm((x-µ)/s) OR P(X<=x)= CDF('normal', x, µ, s) */ /*3. Let X~N(µ, s) then P(X>x)= SDF('normal', x, µ, s) */ /*4. Let Z~N(0, 1) such that p=Pr(Z=z*) then z*=probit(p) OR z*=QUANTILE('Normal', p, 0, 1) */ /*5. Let X~N(µ, s) such that p=Pr(X=x*) then x*=µ+probit(p)*s OR x*=QUANTILE('Normal', p, µ, s) */ /********************************************************************************* **************/ data Q2_2; prob2_a= probnorm((90-100)/15); prob2_b =CDF('normal', 90, 100, 15); prob2_c =1-SDF('normal', 90, 100, 15); run; proc print data=Q2_2; run; data Q2_3; prob3_a= probnorm((90-100)/15); prob3_b =CDF('normal', 90, 100, 15); prob3_c =1-SDF('normal', 90, 100, 15); run; proc print data=Q2_3; run; data Q2_4; prob4_a= 1-probnorm((90-100)/15); prob4_b =1-CDF('normal', 90, 100, 15); prob4_c =SDF('normal', 90, 100, 15); run; proc print data=Q2_4; run; data Q2_5; prob5_a= probnorm((110-100)/15)-probnorm((90-100)/15); prob5_b = CDF('normal', 110, 100, 15)-CDF('normal', 90, 100, 15); prob5_c =SDF('normal', 90, 100, 15)- SDF('normal', 110, 100, 15); run; proc print data=Q2_5; run; data Q2_6; xstar_a= 100+probit(0.90)*15; xstar_b = QUANTILE('Normal', 0.90, 100, 15); run; proc print data=Q2_6; run; data Q2_7; xstar_a= 100+probit(0.10)*15; xstar_b = QUANTILE('Normal', 0.10, 100, 15); run; proc print data=Q2_7; run;