 Okay students, you will have checked in previous slides what are the notations which we use in multi period What are the mean vector and how we perform them and how we find out the correlation matrix Here is the example Now find the mean vector and correlation matrix for the 2 random variables that what is the random variable of the x1 and x2 while the joint probability function f of x1 f of x2 is given by now here is the two random variable x1 and x2 x1 minus 1 0 minus 1 and x2 0 1 this is the joint probability distribution f of x1 f of x1 x1 f of x1 x2 so here we have joint distribution and here you have x1 f of x1 i.e. total we have data given from this data now we have to find its mean vector covariance matrix and correlation matrix and now we have two random variables in the current example more than two will also come to us further current example we have two random variables now the solution x1 x1 we have a random variable minus 1 0 1 f1 f of x1 and you know that the sum of probability which is equals to 1 then further we have x1 multiplied by this x1 multiplied by f of x1 now second x2 the second random variable x2 0 1 and the x2 f of x2 write it down here f2 into x2 now these two multiplication now multiply these column further you have this result and this sum sum of which is x1 f of x1 and sum sum the total is x2 f of x2 total here we have table in that table we have the required results we have to find now find the mean vector okay mean vector mu which is equals to mu1 mu2 mean vector mu vector we do not have we have to find mu1 and mu2 where mu1 this which you have mu1 mu1 which is equals to sum of x1 f of x1 in random variable you must have read all these things you must have an idea that random variable when we are using that random variable according what is the value of mu1 sum x1 f of x1 now sum x1 f of x1 where did it come from 0.10 mu2 second we have the value of the second random variable we have to check the sum x2 f of x2 this sum we have taken from here now the point 10 point 20 mu1 mu2 value now mean vector what happened mu1 mu2 point 10 and point 20 this is the mean vector simple as we find mean so we have this mean vector value now next find the covariance matrix now this is the covariance matrix sigma 11 sigma 12 sigma 21 and sigma 22 this is the covariance matrix how to find the covariance matrix now sigma 11 as we know that the expected value of x1 which is equal to the mu1 now the expected value of x2 which is equal to the mu2 now I raise this sigma 11 so expected value of x1 square minus expected value of x1 whole square now the expected value of x1 which is equal to the mu1 open the expectation expectation we are opening so random variable i.e. x1 expected value of x1 whole square okay now we open it so what do you have random variable square i.e. sum expectation open sum x1 square into its probability so probability what is f1 of x1 so here many notations have written expected value of x1 square how we have opened that unit into its probability so x1 square into its probability minus expected value of x1 now in previous example we have seen that x1 is equal to sum x1 f of x1 now this sum x1 into f of x1 sum x1 into f of x1 whole square and this is equals to the mu mu1 now find how we are doing x1 square x1 square what is your first first this is x1 minus 1 square now minus 1 square multiplied by 0.30 multiplied by 0.30 i.e. minus 1 square multiplied by 0.30 plus 0 square multiplied by 0.3 plus 1 square multiplied by 0.40 so here we have done minus 1 square into 0.3 here multiplied by 0 square into 0.3 plus 1 into 0.4 so 1 into now 1 into 0.4 minus 1 square minus 1 square which is equals to 1 into 0.30 minus 0.1 whole square 0.1 we have basically mu1 so 0.1 we have mu1 okay you solved all these factors so answer is 0.69 we have sigma 11 now find the sigma 22 sum x2 square f of x2 minus sum x2 into f of x2 whole square now f of x2 i.e. this factor you know that which is equal to expected value of x2 and expected value of x2 which is equals to mu now here 0 multiplied by 0.8 plus 1 multiplied by 0.20 0 multiplied by 0.8 plus 1 square into 0.20 0 square you know it is 0 further it is solved so result is sigma 22.1 so you have sigma sigma 11 and sigma 22 now next is the sigma 12 sigma 12 means covariance find now which is equals to expected value of x1 x2 minus expected value of x1 minus x2 journal definition of the covariance which is equals to expected value of x1 x2 minus expected value of x1 into expected value of x2 further you know expected value of x1 which is equals to mu1 expected value of x2 which is equals to mu2 now expected value of x1 x2 open the expected value of x1 x2 so expectation open here we have done sum unit into its probability and this probability is joint probability which is given in the back probability of x1 x2 now you see further how we find it minus 1 into 0 into 0.24 minus 1 into 0 into 0 into 0.24 minus 1 i.e. x1 into x2 into f of x1 x2 minus 1 into 0 into 0.24 so this we have done minus 1 into 0 into 0.24 plus plus 0 into 0 if i have my i means we haveFr Tusso nto 0 into 2.16 plus 0 into 0 into 2.16 plus 0 into 0 into 2.16 then we have minus 1 into 0 into 2.40 toggles to point 1 into point 2 तो सअरा सलूषन अपनके पास आग्या minus 0.088 कोवरयेंच कि बालु नेगीटिप अग्यतीटीटीटीटीटीटीटीटीटी। तो हमारे पास मैं। अप के साम यह आप कैसे लिख लिखच लिखचचच ञानी variance covariance matrix अप क्ते रेत गया सब में की लाऩे साखी दनान Yuriно syndna है। more आम नहीं खिल अप उलतर हैे। string �松 Nan षिग्म सेंटिए छुर सब स्यनालरे है। अप मैर्च भी अप सब सेंटी recordings lime श्प zawszeा ले दो खरी न सेंटा त 알려ं सेंटिरे ॥ धियpe ऻफ तित �可 balm उसिग्मा 1 आन गयाता 0.69 and सिग्मा 2 2 0.16. अनका स्केरूट लेनी हैं थी के ये स्केरूट के वालियो अपने याम पे लिख लीग अप सकेरूट लेने के बात अम ने नेकस क्या करने है लेना है ती कोंगेगाद़ करे लेए भीग बाट़ कोत्तो, दी कोगाद़, ती केखाद़ लगाद़ लेए भीग ने अगर और ँरे. बाट़ ट़्ी कीचिस की बाट़ और थी की ऽगयाद़ कर atmex ki wanawar point 8307 atmex ती केखाद़ रोग उद्वे profile kanhex अगट्TER P अगट्TER P इसाड़े साड़े को नेdamnal issue अगट्TER P इसाड़े कुईता खुईता बाता तुर्ची have mixed many numbers of numbers of numbers. अगट्TER P पागट्TER P यपंद्टी औगट्TER P आद्टादे औगट्TER P 2 कॉ मेट्रिक्स है. तो, तु रेस्छलत हमारे बस क्या जैगा. ये रेस्छल, विछ ये सेखपल्स तु अं तु तु कर रेस्छल ता एका. दें ये 2 इंटू तु मेट्रिक्स हागी एक. दें मूल्टीप्LYप भा देस मेट्रिक्स, दींवार्च मेट्रिक्स, cock it up. enjoys one more employ a plan. ६ौॢैॐौ८फ़ॕ२ौ।ै।॑ुॐ।ौ।।।।।।।।ु।।।।।।।।।७।।।।।।।।।।।।।। 0 multiplied by any value which is equal to zero. unique d contenido fail row will multiply by first column, first row multiplied by second column, u need to solve with this correlation matrix.