Qo`shish va ko`paytirish teoremalarning natijalari. Birgalikda bo`lgan hodisalar ehtimollari uchun qo`shish teoremasi. To`la ehtimol formulasi

Erkli sinashlarda hodisa ro‘y berish sonining matematik kutilishi.
Teorema. n ta erkli sinashda A hodisa ro‘y berish sonining matematik kutilishi sinashlar soninihar bir sinashda hodisaning ro‘y berish ehtimoliga ko‘paytirilganiga teng:⁹
M(X)=np.
Isboti. X tasodifiy miqdor sifatida n ta erkli sinashda A hodisaning ro‘y berish sonini olamiz.
Ko‘rinib turibdiki, bu sinashlarda A hodisa ro‘y berishining X umumiy soni shu hhodisaning ayrim sinashlarda ro‘y berish sonlari yig‘indisidan iborat. Shuning uchun agar X₁ birinchi sinashda,
X₂- ikkinchi sinashda, ... , X_n n- sinashdaro‘y berish soni bo‘lsa, u holda hodisa ro‘y berishining umumiy soni X=X₁+X₂+ ... +X_n bo‘ladi.
Matematik kutilishning uchinchi xossasiga sosan:

1^ Prassana Sahoo, Probability and mathematical statistics, - USA, University of Louisville, KY40292, 2013. – 712 p.

2^ Prassana Sahoo, Probability and mathematical statistics, - USA, University of Louisville, KY40292, 2013. – 712 p.

3^ Alpha C. Chiang, Kevin Wainwright. Fundamental methods of Mathematical Economics.-New York; McGraw-Hill Irwin. 2003,-700 p.

4^ Alpha C. Chiang, Kevin Wainwright. Fundamental methods of Mathematical Economics.-New York; McGraw-Hill Irwin. 2003,-700 p.

5^ Muxitdinov T., Sagdullayev D., Shoraxmetov Sh. Ehtimollar nazariyasi va matematik statistika fanidan masalalar to’plami.-T.: 2005.-150 bet.

6^ Muxitdinov T., Sagdullayev D., Shoraxmetov Sh. Ehtimollar nazariyasi va matematik statistika fanidan masalalar to’plami.-T.: 2005.-150 bet.

7^ J.S.Milton Jesse C, Arnold. Introduction to probability and statistics. New York. McGraw-Hill Book Co. 1995 e. – 810 p.

8^ J.S.Milton Jesse C, Arnold. Introduction to probability and statistics. New York. McGraw-Hill Book Co. 1995 e. – 810 p.

9^ J.S.Milton Jesse C, Arnold. Introduction to probability and statistics. New York. McGraw-Hill Book Co. 1995 e. – 810 p.