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We prove that for every $b$ there exists (explicitly given) $\\lambda_b \\in (1/b, 1)$ such that the Hausdorff dimension of the graph of $W_{\\lambda, b}$ is equal to $D = 2+\\frac{\\log\\lambda}{\\log b}$ for every $\\lambda\\in(\\lambda_b,1)$. We also show that the dimension is equal to $D$ for almost every $\\lambda$ on some larger interval. 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We prove that for every $b$ there exists (explicitly given) $\\lambda_b \\in (1/b, 1)$ such that the Hausdorff dimension of the graph of $W_{\\lambda, b}$ is equal to $D = 2+\\frac{\\log\\lambda}{\\log b}$ for every $\\lambda\\in(\\lambda_b,1)$. We also show that the dimension is equal to $D$ for almost every $\\lambda$ on some larger interval. 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