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Answer to Question #5409 in Statistics and Probability for Angela

Question #5409
A random variable X has the following distribution:
Value (x) -3 -2 0 1 2
Prob. p(x) 2/9 1/9 p 2/9 p2
Find p and P(|X+1|>1).
Expert's answer
We have distribution of X

Thus

<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeUAAAAuCAIAAACZCpb2AAAFxklEQVR4nO2dXZaDIAyFXZcLYj2shs24mM7DaKtUfgIRkvR+T3POtJiEeAUkdHkBAADQwDLbAAAAAFVArwEAQAfQawAA0AH0GgAAdAC9BgAAHUCvAQBAB1m93vy6uPAKbllWv40ySQ7BLTsu9Le2+VVmHHndBFPZ/LqY7s7gRN5ERFq9yOv15r33zoVXcCb7Psfm193n/1ugLwCHJopLNV43wWSsy3VwEm8iKu1e5NdDgl9XF16v4NSHiErwJ483vzKk/+ZXcan2gJtgHsbHVcE5L/AmItLjRVavD5k2ngUVBGdUr6+wuAmmcczibPZhcC4ouIkK9HmR0+tDpm3MQXrYF/IZWhEdRh43wSTOayH2NHtXI/E3UZ5eL7A/pILNrxwpIj3VmNwEs9mF25Jiv6f40m+iLP1eQK/LcK3eC0+1H3xJYRhTS1ub9+H9p+ibKAeHF9DrAp/9ExxNiU01RjeBCIIzo9efDaea13tYvIBeZzmPOU+Pxzbk6jWrm0AERjcJyL2JKDCMr69vKwroj1gF8QOxN/+F1h1xuwnmY/dVBPT6xPvWzbUlVHZ4uXl6denYWRQFBY/bzTxchZTjK0XHlID2+XXuyxHBmVMWC72+UtMLm3ejIya2mBtUwlVIOb5S9LMS/GRBkdgK2FvGxATE3K1ffx7UqdwZvDYmP5V530oyBldMa6yFlEMHWdt2utCzp1eoGTwOjAk4k3rfWLUyMhKGVH4wr6DXNDp3m01Lhoe30UzWa5Ex6cXW0ySzP+QzzJbQHYRU/t448/7i/7/4+2+sXh89s5+dmOuisXpda1hvIeWcZLh9iUfoi6orjBAXVTGphcWpKZZTyO/nK6+MfH/2IVc5U5lftcePr4Nb1nVXvUxsxo+vKwxL7F643aB6m0fjk+H0Mu87AgWX5/jVg6SYsFF715cTeILxB+X915Spa6WIXBuflcrdEyXGbiM3FdyyurBbH8eGN59orWUNOz7S25GzkuFfoeIPVrhcye2Xp6mDjJgwU3RKrOWv16tCryk315Ou8kyBzx9It5a4P5ZlSYUrN/AktlY1Ir4Ur+VCw2hYlW1Fw1gG/COToXjl6r5oar0OWleqikmta0xOjbGc1l/nNrP/pW27z7rauweQR/5trF9fI52dAA1eDykZli2kHD3ZakqGrzLvcl9oWg+RFxMGCE5V3VlC10OIJxDUi8jlO+NS2cz+kNNjNLh8mgx/35gxjK+QkqFkq3kvRPQtQl9UGaVyf8iTMemF5JQoy+9I6jW5ojXran8iyq6qHKrXl6LE8mfH6XXGML5CyuGVotkLUvqi4zLSGBST0ci3PKHX9MO9Cq52VdioSuXHEXs2hFjDnuMHXS6iNyYKLL/V64p3jLH+Flw1eljYDMQmlVjDnuMHXS6iNyYaLP/W6yqrY0U3KteMVZ4sTX0mGnyJJdYw4ch0eW5d8qMxedS1Jy2/P5Lpa4Ww6sKxXtcshESnP5RdDSp/APL0yrR38ZyxKV7EGgYaMNybal37vPLZLsecfe20qHPpotc3L4WS6Bww1xOVTFOqhh5sihexhoEGDPemXtdSx5yFEG2dqnwCnfQ6ubfuDj0PuEainIjmFLOa4kWsYaABw71pxbX0hu5aPcXvgSWIZl29es3UFC9iDQMNGO5NI66ljjkj1JBDr1NcF927Fs0Ym+JFrGGgAcO9acK11KYMypEf0Os08XJ+xxOdsSlexBoGGjDcm/pdS8ky6fiz9Mk+N8d9XN9w/hCM5zrMPyIigVjDQAOGe1Ola+nKYNppldTxNW99sw6g1kAXhntTpWuZY86Ihwvf63V6gejX9JpxSiF2diLWMNCA4d7U6Vr2mDPqWfDJ80MSUfkZvT7Wyxie5YxN8SLWMNCA4d5U61rpmDPyT3ekxtcuRNfa2/0ZvQYAAGEkzntyIX42QK8BAGAqyZ8LSuwU1DktAQAA/WD/NQAA6AB6DQAAOvgDVml+ag2wnYoAAAAASUVORK5CYII=" alt="">

As a result we have that X has the following distribution

Value (x) -3 & -2 0 & 1 2

Prob. p(x) 2/9 1/9 4/27 2/9 8/27

Hence

<img src="data:image/png;base64,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" alt="">



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