Mixing
calculating sum of binomial probabilities P{A+C}
$begingroup$
i have a simple question about calculating the sum of two binomials: say i have 2 events: $A ~ B(n,p)$; $C ~ B(m, p)$ and i want to calculate P(A+C). is this the way to do it? we'll call $A+C=D$, then $D~B(n+m,p)$, so $P(D)=sum_{i=0} ^D binom ni p^i(1-p)^{i-x}binom m{D-i}p^{D-i}(1-p)^{m+i-D}$ ? is this correct?
basically, i need to check if D,A are independent, and i can do that only by showing that P{A=n,D=0} is not equal to P{A=n}P{D=0}, but what is really important to me is knowing if the way i wrote the probability of D is correct.
thank you very much
probability probability-distributions
asked Jan 28 at 13:15
q123q123
75
$endgroup$
add a comment |
$begingroup$
i have a simple question about calculating the sum of two binomials: say i have 2 events: $A ~ B(n,p)$; $C ~ B(m, p)$ and i want to calculate P(A+C). is this the way to do it? we'll call $A+C=D$, then $D~B(n+m,p)$, so $P(D)=sum_{i=0} ^D binom ni p^i(1-p)^{i-x}binom m{D-i}p^{D-i}(1-p)^{m+i-D}$ ? is this correct?
basically, i need to check if D,A are independent, and i can do that only by showing that P{A=n,D=0} is not equal to P{A=n}P{D=0}, but what is really important to me is knowing if the way i wrote the probability of D is correct.
thank you very much
probability probability-distributions
asked Jan 28 at 13:15
q123q123
75
$endgroup$
add a comment |
$begingroup$
i have a simple question about calculating the sum of two binomials: say i have 2 events: $A ~ B(n,p)$; $C ~ B(m, p)$ and i want to calculate P(A+C). is this the way to do it? we'll call $A+C=D$, then $D~B(n+m,p)$, so $P(D)=sum_{i=0} ^D binom ni p^i(1-p)^{i-x}binom m{D-i}p^{D-i}(1-p)^{m+i-D}$ ? is this correct?
basically, i need to check if D,A are independent, and i can do that only by showing that P{A=n,D=0} is not equal to P{A=n}P{D=0}, but what is really important to me is knowing if the way i wrote the probability of D is correct.
thank you very much
probability probability-distributions
asked Jan 28 at 13:15
q123q123
75
$endgroup$
i have a simple question about calculating the sum of two binomials: say i have 2 events: $A ~ B(n,p)$; $C ~ B(m, p)$ and i want to calculate P(A+C). is this the way to do it? we'll call $A+C=D$, then $D~B(n+m,p)$, so $P(D)=sum_{i=0} ^D binom ni p^i(1-p)^{i-x}binom m{D-i}p^{D-i}(1-p)^{m+i-D}$ ? is this correct?
basically, i need to check if D,A are independent, and i can do that only by showing that P{A=n,D=0} is not equal to P{A=n}P{D=0}, but what is really important to me is knowing if the way i wrote the probability of D is correct.
thank you very much
probability probability-distributions
probability probability-distributions
asked Jan 28 at 13:15
q123q123
75
asked Jan 28 at 13:15
q123q123
75
asked Jan 28 at 13:15
q123q123
75
asked Jan 28 at 13:15
q123q123
75
asked Jan 28 at 13:15
q123q123
75
75
add a comment |
add a comment |
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